CHAPTER 4 USING A CALCULATOR
EXERCISE 12 Page 26
1.
Evaluate 378.37 – 298.651 + 45.64 – 94.562
By calculator, 378.37 – 298.651 + 45.64 – 94.562 = 30.797
2.
Evaluate 25.63 × 465.34 correct to 5 significant figures.
By calculator, 25.63 × 465.34 = 11 926.6642 = 11 927, correct to 5 significant figures
3.
Evaluate 562.6 ÷ 41.3 correct to 2 decimal places.
By calculator, 562.6 ÷ 41.3 = 13.622276... = 13.62, correct to 2 decimal places
4.
Evaluate
By calculator,
5.
17.35 × 34.27
correct to 3 decimal places.
41.53 ÷ 3.76
17.35 × 34.27
= 53.83187... = 53.832, correct to 3 decimal places
41.53 ÷ 3.76
Evaluate 27.48 + 13.72 × 4.15 correct to 4 significant figures.
By calculator, 27.48 + 13.72 × 4.15 = 84.418 = 84.42, correct to 4 significant figures
6.
Evaluate
By calculator,
7.
( 4.527 + 3.63)
( 452.51 ÷ 34.75)
( 4.527 + 3.63)
( 452.51 ÷ 34.75)
Evaluate 52.34 −
+ 0.468 correct to 5 significant figures.
+ 0.468 = 1.0944077 ... = 1.0944, correct to 5 significant figures
( 912.5 ÷ 41.46 )
( 24.6 − 13.652 )
correct to 3 decimal places.
47
© 2014, John Bird
By calculator, 52.34 −
8.
Evaluate
( 912.5 ÷ 41.46 )
( 24.6 − 13.652 )
= 50.329663... = 50.330, correct to 3 decimal places
52.14 × 0.347 ×11.23
correct to 4 significant figures.
19.73 ÷ 3.54
By calculator,
52.14 × 0.347 ×11.23
= 36.45494 ... = 36.45, correct to 4 significant figures
19.73 ÷ 3.54
9.
451.2 363.8
correct to 4 significant figures.
−
24.57 46.79
Evaluate
By calculator,
10. Evaluate
By calculator,
451.2 363.8
= 10.58869... = 10.59, correct to 4 significant figures
−
24.57 46.79
45.6 − 7.35 × 3.61
correct to 3 decimal places.
4.672 − 3.125
45.6 − 7.35 × 3.61
= 12.324822... = 12.325, correct to 3 decimal places
4.672 − 3.125
48
© 2014, John Bird
EXERCISE 13 Page 27
1.
Evaluate 3.52
By calculator, 3.52 = 12.25
2.
Evaluate 0.192
By calculator, 0.192 = 0.0361
3.
Evaluate 6.852 correct to 3 decimal places.
By calculator, 6.852 = 46.9225 = 46.923, correct to 3 decimal places
4.
Evaluate ( 0.036 ) in engineering form.
2
By calculator, ( 0.036 ) = 0.001296 = 1.296 ×10−3 in engineering form
2
5.
Evaluate 1.5632 correct to 5 significant figures.
By calculator, 1.5632 = 2.442969 = 2.4430, correct to 5 significant figures
6.
Evaluate 1.33
By calculator, 1.33 = 2.197
7.
Evaluate 3.143 correct to 4 significant figures.
By calculator, 3.143 = 30.959144 = 30.96, correct to 4 significant figures
8.
Evaluate ( 0.38 ) correct to 4 decimal places.
3
By calculator, ( 0.38 ) = 0.054872 = 0.0549, correct to 4 decimal places
3
49
© 2014, John Bird
9.
Evaluate
( 6.03)
3
correct to 2 decimal places.
By calculator, ( 6.03) = 219.256227 = 219.26, correct to 2 decimal places
3
10.
Evaluate
( 0.018)
3
in engineering form.
By calculator, ( 0.018 ) = 5.832 ×10−6 in engineering form
3
50
© 2014, John Bird
EXERCISE 14 Page 28
1.
Evaluate
1
correct to 3 decimal places.
1.75
By calculator,
1
= 0.5714285 ... = 0.571, correct to 3 decimal places
1.75
2.
1
0.0250
Evaluate
By calculator,
1
= 40
0.0250
3.
1
correct to 5 significant figures.
7.43
Evaluate
By calculator,
1
= 0.1345895... = 0.13459, correct to 5 significant figures
7.43
4.
1
correct to 1 decimal place.
0.00725
Evaluate
By calculator,
1
= 137.93103... = 137.9, correct to 1 decimal place
0.00725
5.
1
1
correct to 4 significant figures.
−
0.065 2.341
Evaluate
By calculator,
6.
1
1
= 14.957447... = 14.96, correct to 4 significant figures
−
0.065 2.341
Evaluate 2.14
By calculator, 2.14 = 19.4481
51
© 2014, John Bird
7.
Evaluate
( 0.22 )
5
correct to 5 significant figures in engineering form.
By calculator, ( 0.22 ) = 5.153632 ×10−4 = 515.36 ×10−6 , correct to 5 significant figures in
5
engineering form
8.
Evaluate (1.012 ) correct to 4 decimal places.
7
By calculator, (1.012 ) = 1.087085... = 1.0871, correct to 4 decimal places
7
9.
Evaluate
( 0.05)
6
in engineering form.
By calculator, ( 0.05 ) = 15.625 ×10−9 in engineering form
6
10.
Evaluate 1.13 + 2.94 − 4.42 correct to 4 significant figures.
By calculator, 1.13 + 2.94 − 4.42 = 52.6991 = 52.70, correct to 4 significant figures
52
© 2014, John Bird
EXERCISE 15 Page 29
1.
Evaluate
4.76 correct to 3 decimal places.
By calculator,
4.76 = 2.181742... = 2.182, correct to 3 decimal places
2.
123.7 correct to 5 significant figures.
Evaluate
By calculator, 123.7 = 11.122050 = 11.122, correct to 5 significant figures
3.
Evaluate
34 528 correct to 2 decimal places.
By calculator,
34 528 = 185.81711... = 185.82, correct to 2 decimal places
4.
0.69 correct to 4 significant figures.
Evaluate
By calculator,
0.69 = 0.83066238... = 0.8307, correct to 4 significant figures
5.
0.025 correct to 4 decimal places.
Evaluate
By calculator,
6.
Evaluate
0.025 = 0.15811388... = 0.1581, correct to 4 decimal places
3
17 correct to 3 decimal places.
By calculator, 3 17 = 2.57128159... = 2.571, correct to 3 decimal places
7.
Evaluate
By calculator,
4
773 correct to 4 significant figures.
4
773 = 5.2728434... = 5.273, correct to 4 significant figures
53
© 2014, John Bird
5
3.12 correct to 4 decimal places.
By calculator,
5
3.12 = 1.2555410... = 1.2555, correct to 4 decimal places
9.
3
0.028 correct to 5 significant figures.
3
0.028 = 0.30365889... = 0.30366, correct to 5 significant figures
8.
Evaluate
Evaluate
By calculator,
10.
By calculator,
11.
6
Evaluate
6
2451 − 4 46 correct to 3 decimal places.
2451 − 4 46 = 1.0676068... = 1.068, correct to 3 decimal places
Evaluate 5 ×10−3 × 7 ×108 and express in engineering form.
By calculator, 5 ×10−3 × 7 ×108 = 3.5 ×106 in engineering form
12.
Evaluate
By calculator,
13.
Evaluate
By calculator,
14.
Evaluate
By calculator,
3 ×10−4
and express in engineering form.
8 ×10−9
3 ×10−4
= 37.5 ×103 in engineering form
8 ×10−9
6 ×103 ×14 ×10−4
and express in engineering form.
2 ×106
6 ×103 ×14 ×10−4
= 4.2 ×10−6 in engineering form
2 ×106
56.43 ×10−3 × 3 × 104
correct to 3 decimal places in engineering form.
8.349 ×103
56.43 ×10−3 × 3 × 104
= 0.202766798... = 202.767 ×10−3 , correct to 3 decimal places
8.349 ×103
54
© 2014, John Bird
in engineering form
15.
Evaluate
99 ×105 × 6.7 ×10−3
correct to 4 significant figures in engineering form.
36.2 ×10−4
99 ×105 × 6.7 ×10−3
= 18 323 204.42 = 18 320 000 = 18.32 ×106 correct to 4
36.2 ×10−4
significant figures in engineering form
By calculator,
55
© 2014, John Bird
EXERCISE 16 Page 30
1.
Evaluate
By calculator,
2.
Evaluate
By calculator,
3.
4 1
− as a decimal, correct to 4 decimal places.
5 3
4 1
− = 0.466666... = 0.4667, correct to 4 decimal places
5 3
2 1 3
− + as a fraction.
3 6 7
2 1 3 13
− + =
3 6 7 14
5 5
Evaluate 2 + 1 as a decimal, correct to 4 significant figures.
6 8
5 5 107
By calculator, 2 + 1 = = 4.4583333... = 4.458, correct to 4 significant figures
6 8 24
6
1
4. Evaluate 5 − 3 as a decimal, correct to 4 significant figures.
7
8
6
1 153
By calculator, 5 − 3 = = 2.7321428... = 2.732, correct to 4 significant figures
7
8 56
5.
Evaluate
By calculator,
6.
Evaluate
By calculator,
1 3 8
as a fraction.
− ×
3 4 21
1 3 8
1
− ×
=
3 4 21 21
3 5 1
+ − as a decimal, correct to 4 decimal places.
8 6 2
3 5 1 17
+ − = = 0.70833333... = 0.7083, correct to 4 decimal places
8 6 2 24
56
© 2014, John Bird
7.
Evaluate
By calculator,
8.
3 4 2 4
× − ÷ as a fraction.
4 5 3 9
3 4 2 4
9
× − ÷ = −
4 5 3 9
10
8
2
Evaluate 8 ÷ 2 as a mixed number.
9
3
1
8
2 10
By calculator, 8 ÷ 2 == 3
3
9
3 3
9.
1 1
7
Evaluate 3 ×1 − 1 as a decimal, correct to 3 decimal places.
5 3 10
1 1
7 77
By calculator, 3 ×1 − 1 = = 2.566666... = 2.567, correct to 3 decimal places
5 3 10 30
 1 2
 4 −1  2
5 3
10. Evaluate 
− as a decimal, correct to 3 significant figures.
3 9
 1
3 × 2 
5
 4
 1 2
 4 − 1  2 118
5 3
By calculator, 
= 0.07758053... = 0.0776, correct to 3 significant figures
− =
3  9 1521
 1
3 × 2 
5
 4
57
© 2014, John Bird
EXERCISE 17 Page 31
1.
Evaluate sin 67° correct to 4 decimal places.
By calculator, sin 67° = 0.9205, correct to 4 decimal places
2.
Evaluate cos 43° correct to 4 decimal places.
By calculator, cos 43° = 0.7314, correct to 4 decimal places
3.
Evaluate tan 71° correct to 4 decimal places.
By calculator, tan 71° = 2.9042, correct to 4 decimal places
4.
Evaluate sin 15.78° correct to 4 decimal places.
By calculator, sin 15.78° = 0.2719, correct to 4 decimal places
5.
Evaluate cos 63.74° correct to 4 decimal places.
By calculator, cos 63.74° = 0.4424, correct to 4 decimal places
6.
Evaluate tan 39.55° – sin 52.53° correct to 4 decimal places.
By calculator, tan 39.55° – sin 52.53° = 0.0321, correct to 4 decimal places
7.
Evaluate sin(0.437 rad) correct to 4 decimal places.
By calculator, sin(0.437 rad) = 0.4232, correct to 4 decimal places
8.
Evaluate cos(1.42 rad) correct to 4 decimal places.
By calculator, cos(1.42 rad) = 0.1502, correct to 4 decimal places
58
© 2014, John Bird
9.
Evaluate tan(5.673 rad) correct to 4 decimal places.
By calculator, tan(5.673 rad) = –0.6992, correct to 4 decimal places
10. Evaluate
By calculator,
( sin 42.6° )( tan 83.2° )
cos 13.8°
( sin 42.6° )( tan 83.2° )
cos 13.8°
correct to 4 decimal places.
= 5.8452, correct to 4 decimal places
59
© 2014, John Bird
EXERCISE 18 Page 31
1.
Evaluate 1.59π correct to 4 significant figures.
By calculator, 1.59π = 4.995, correct to 4 significant figures
2.
Evaluate 2.7(π – 1) correct to 4 significant figures.
By calculator, 2.7(π – 1) = 5.782, correct to 4 significant figures
3.
Evaluate π 2
(
By calculator, π 2
4.
)
13 − 1 correct to 4 significant figures.
(
)
13 − 1 = 25.72, correct to 4 significant figures
Evaluate 3eπ correct to 4 significant figures.
By calculator, 3eπ = 69.42, correct to 4 significant figures
5.
Evaluate 8.5e −2.5 correct to 4 significant figures.
By calculator, 8.5e −2.5 = 0.6977, correct to 4 significant figures
6.
Evaluate 3e 2.9 − 1.6 correct to 4 significant figures.
By calculator, 3e 2.9 − 1.6 = 52.92, correct to 4 significant figures
7.
Evaluate 3e( 2π −1) correct to 4 significant figures.
By calculator, 3e( 2π −1) = 591.0, correct to 4 significant figures
π
8.
Evaluate 2π e 3 correct to 4 significant figures.
π
By calculator, 2π e 3 = 17.90, correct to 4 significant figures
60
© 2014, John Bird
9.
Evaluate
5.52π


 −2
 correct to 4 significant figures.
 2 e × 26.73 
By calculator,
5.52π


 −2
 = 3.520, correct to 4 significant figures
 2 e × 26.73 
10. Evaluate
 e( 2 − 3 ) 

 correct to 4 significant figures.
π
×
8.57


By calculator,
 e( 2 − 3 ) 

 = 0.3770, correct to 4 significant figures
 π × 8.57 
61
© 2014, John Bird
EXERCISE 19 Page 33
1. Given 25 × 0.06 × 1.4 = 0.21 state which type of error, or errors, have been made.
Order of magnitude error – should be 2.1
2. Given 137 × 6.842 = 937.4 state which type of error, or errors, have been made.
Rounding-off error – should add ‘correct to 4 significant figures’ or ‘correct to 1 decimal place’
3. Given
24 × 0.008
= 10.42 state which type of error, or errors, have been made.
12.6
Blunder
(
24 × 0.008
= 0.015238... )
12.6
4. For a gas pV = c. When pressure p and volume V are measured as p = 103 400 Pa and V = 0.54 m3,
then c = 55 836 Pa/m3. State which type of error, or errors, have been made.
Measured values, hence c = 55 800 Pa/m3
5. Given
4.6 × 0.07
= 0.225 state which type of error, or errors, have been made.
52.3 × 0.274
Order of magnitude error and rounding-off error – should be 0.0225, correct to 3 significant figures,
or 0.0225, correct to 4 decimal places
6. Evaluate 4.7 × 6.3 approximately, without using a calculator.
4.7 × 6.3 ≈ 5 × 6 ≈ 30 (29.61 by calculator)
7. Evaluate
2.87 × 4.07
approximately, without using a calculator.
6.12 × 0.96
62
© 2014, John Bird
2.87 × 4.07 3 × 4 12
≈2
≈
≈
6.12 × 0.96 6 × 1 6
8. Evaluate
(1.98817… by calculator)
72.1×1.96 × 48.6
approximately, without using a calculator.
139.3 × 5.2
72.1×1.96 × 48.6 70 × 2 × 50 50
≈ 10
≈
≈
139.3 × 5.2
140 × 5
5
(9.48141… by calculator)
63
© 2014, John Bird
EXERCISE 20 Page 33
1. State whether the following number is rational or irrational: 1.5
1.5 is a rational number as it can be expressed as a fraction (i.e. 3/2)
2. State whether the following number is rational or irrational:
3
3 is an irrational number as it cannot be expressed as a fraction
3. State whether the following number is rational or irrational:
5
8
5
is a rational number as it is a fraction
8
4. State whether the following number is rational or irrational: 0.002
0.002 is a rational number as it can be expressed as a fraction (i.e. 2/1000)
5. State whether the following number is rational or irrational: π 2
π 2 is an irrational number as it cannot be expressed as a fraction
6. State whether the following number is rational or irrational: 11
11 is a rational number as it can be expressed as a ratio (i.e. 11/1)
7. State whether the following number is rational or irrational:
6
0
6
is an irrational number as it is infinite
0
64
© 2014, John Bird
8. State whether the following number is rational or irrational:
16
16 is a rational number as it can be expressed as a fraction (i.e. 4/1)
9. State whether the following number is rational or irrational: 0.11
0.11 is a rational number as it can be expressed as a fraction (i.e. 11/100)
10. State whether the following number is rational or irrational:
( 2)
( 2)
2
2
is a rational number as it can be expressed as a fraction (i.e. 2/1)
65
© 2014, John Bird
EXERCISE 21 Page 34
1. The area A of a rectangle is given by the formula A = lb. Evaluate the area when l = 12.4 cm and
b = 5.37 cm.
Area, A = l × b = 12.4 × 5.37 = 66.588 cm2 = 66.59 cm2
2. The circumference C of a circle is given by the formula C = 2πr. Determine the circumference
given r = 8.40 mm.
Circumference, C = 2πr = 2 × π × 8.40 = 52.78 mm
3. A formula used in connection with gases is R =
PV
. Evaluate R when P = 1500, V = 5 and
T
T = 200
R = (PV)/T =
(1500)(5)
= 37.5
200
4. The velocity of a body is given by v = u + at. The initial velocity u is measured when time t is
15 seconds and found to be 12 m/s. If the acceleration a is 9.81 m/s2 calculate the final velocity v.
Velocity, v = u + at = 12 + 9.81 × 15 = 159 m/s
5. Calculate the current I in an electrical circuit when I = V/R amperes when the voltage V is
measured and found to be 7.2 V and the resistance R is 17.7 Ω.
Current, I =
7.2
V
= 0.407 A
=
R 17.7
6. Find the distance s, given that s =
1 2
gt . Time t = 0.032 seconds and acceleration due to gravity
2
g = 9.81 m/s2. Give the answer in millimetres.
66
© 2014, John Bird
1
1
2
Distance, s = gt 2 = ( 9.81)( 0.032 ) = 0.00502 m or 5.02 mm (since 1 m = 1000 mm)
2
2
7. The energy stored in a capacitor is given by E =
1
CV2 joules. Determine the energy when
2
capacitance C = 5 × 10 − 6 farads and voltage V = 240 V.
Energy, E =
1
1
CV2 = × 5 ×10−6 × 2402 = 0.144 J
2
2
8. Find the area A of a triangle, given A =
1
bh, when the base length l is 23.42 m and the height h is
2
53.7 m.
Area of triangle, A =
1
1
bh = × 23.42 × 53.7 = 628.8 m2
2
2
9. Resistance R 2 is given by R 2 = R 1 (1 + αt). Find R 2 , correct to 4 significant figures, when R 1 =
220,
α = 0.00027 and t = 75.6
Resistance, R2 = R1 (1 + α t )= 220 1 + ( 0.00027 )( 75.6 ) = 220 [1 + 0.020412]
= 220 × 1.020412
= 224.5, correct to 4 significant figures
10. Density =
mass
. Find the density when the mass is 2.462 kg and the volume is 173 cm3. Give
volume
the answer in units of kg/m3.
Volume = 173 cm3 = 173 ×10−6 m3
Density =
mass
2.462 kg
= 14231.21387 = 14 230 kg/m3, correct to 4 significant figures
=
−
6
3
volume 173 ×10 m
67
© 2014, John Bird
11. Velocity = frequency × wavelength. Find the velocity when the frequency is 1825 Hz and the
wavelength is 0.154 m.
Velocity = frequency × wavelength = 1825 × 0.154 = 281.1 m/s
12. Evaluate resistance R T , given
1
1
1
1
when R 1 = 5.5 Ω, R 2 = 7.42 Ω and
=
+
+
RT
R1 R2 R3
R3 = 12.6 Ω.
1
1
1
1
1
1
1
= +
+
=
+
+
= 0.181818 + 0.134771 + 0.079365 = 0.395954
RT R1 R2 R3 5.5 7.42 12.6
and
RT =
1
= 2.526 Ω
0.395954
68
© 2014, John Bird
EXERCISE 22 Page 36
1. Find the total cost of 37 calculators costing £12.65 each and 19 drawing sets costing £6.38 each.
Total cost = 37 × 12.65 + 19 × 6.38 = £589.27
force × distance
. Find the power when a force of 3760 N raises an object a distance of
time
2. Power =
4.73 m in 35 s.
Power =
force × distance 3760 × 4.73
= 508.1 W
=
time
35
3. The potential difference, V volts, available at battery terminals is given by V = E – Ir. Evaluate V
when E = 5.62, I = 0.70 and R = 4.30
Potential difference, V = E – Ir = 5.62 – 0.70 × 4.30 = 5.62 – 3.01 = 2.61 V
4. Given force F =
Force, F =
1
m(v2 – u2), find F when m = 18.3, v = 12.7 and u = 8.24
2
1
1
1
m=
− 8.242 )
( v 2 − u 2 ) (18.3)(12.72=
(18.3)( 93.3924 )
2
2
2
= 854.5, correct to 4 significant figures.
5. The current I amperes flowing in a number of cells is given by I =
nE
. Evaluate the current
R + nr
when n = 36, E = 2.20, R = 2.80 and r = 0.50
nE
(36)(2.20)
79.2
79.2
Current, I ==
= 3.81 A, correct to 3 significant
= =
R + n r 2.80 + (36)(0.50) 2.80 + 18 20.80
figures.
6. The time, t seconds, of oscillation for a simple pendulum is given by t = 2π
l
.
g
Determine the time when l = 54.32 and g = 9.81
69
© 2014, John Bird
(
)
54.32
l
Time,
t = 2π
2=
(6.284)=
5.5372069... (6.284)(2.353127...)
=
( 3.142 )
9.81
g
= 14.79 s, correct to 4 significant figures
7. Energy, E joules, is given by the formula E =
1 2
LI . Evaluate the energy when L = 5.5 and I = 1.2
2
1
1
1
2
Energy,
E = LI 2 =
=
( 5.5)(1.2 )
( 5.5)(1.44 ) = 3.96 J
2
2
2
8. The current I amperes in an a.c. circuit is given by I =
V
. Evaluate the current when
(R2 + X 2 )
V = 250, R = 11.0 and X = 16.2
Current, I =
V
=
R2 + X 2
250
=
11.02 + 16.22
250
250
=
383.44 19.581624...
= 12.77 A, correct to 4 significant figures
9. Distance s metres is given by the formula s = ut +
1 2
at . If u = 9.50, t = 4.60 and a = –2.50,
2
evaluate the distance.
Distance, s = ut +
1 2
1
at = (9.50)(4.60) + (−2.50)(4.60) 2 = 43.7 − 26.45 = 17.25 m
2
2
10. The area, A, of any triangle is given by A =
[ s( s − a)( s − b)( s − c)]
where s =
a+b+c
.
2
Evaluate the area, given a = 3.60 cm, b = 4.00 cm and c = 5.20 cm.
s=
a + b + c 3.60 + 4.00 + 5.20 12.80
=
= = 6.40
2
2
2
Hence, area A =
s ( s − a )( s − b)(
=
s − c)
6.40(6.40 − 3.60)(6.40 − 4.00)(6.40 − 5.20)
=
6.40(2.80)(2.40)(1.20) = 51.6096
= 7.184 cm2, correct to 4 significant figures
70
© 2014, John Bird
11. Given that a = 0.290, b = 14.86, c = 0.042, d = 31.8 and e = 0.650, evaluate v given that
v=
 ab d 
 − 
 c e
ab d
v ==
−
c e
(0.290)(14.86) 31.8
=
−
0.042
0.650
102.60476... − 48.923076...
=
53.68168...
= 7.327 correct to 4 significant figures
12. Deduce the following information from the train timetable shown in Table 4.1.
(a) At what time should a man catch a train at Fratton to enable him to be in London Waterloo
by 14.23 h?
(b) A girl leaves Cosham at 12.39 h and travels to Woking. How long does the journey take?
If the distance between Cosham and Woking is 55 miles, calculate the average speed of the
train.
(c) A man living at Havant has a meeting in London at 15:30 h. It takes around 25 minutes on the
underground to his destination from London waterloo. What train should he catch from
Havant to comfortably make the meeting?
(d) Nine trains leave Portsmouth harbour between 12:18 h and 13:15 h. Which train should be
taken for the shortest journey time?
71
© 2014, John Bird
Table 4.1
(a) Scan down the left of the timetable to find Fratton, and then move to the bottom to find a train
72
© 2014, John Bird
time arrival time 14.23 h at Waterloo (Note that the time is shown as 14:23, which is the 24hour clock; 14:23 means 2.23 p.m.). Now move up from 14:23 to Fratton where the train is seen
to leave at 12.53 h
(b) Scan down the left of the timetable to find Cosham, and then move to the right to find the
12:39 h train. Now move down from 12:39 until reaching Woking, where the train arrives at
14:19 h and 12:39 h to 14:19 h is a journey of 1 hour 40 minutes.
The average speed of the journey is:
55 miles
= 33 m.p.h.
 40 
1  hour
 60 
(c) To be at the meeting by 15:30 h with a 25-minute walk from the station means that the man’s
train should arrive at Waterloo no later than around 15:00 h.
Scan down the left of the timetable to find Havant, and then move to the right to find the train
closest to arriving at Waterloo around 15:00 h. It is seen that the 13:02 h train would arrive in
Waterloo by 14:51, leaving sufficient time to arrive at his 15:30 h meeting.
(d) 12:18 to 14:40 = 2 h 22 min
12:22 to 14:24 = 2 h 2 min
12:22 to 14:49 = 2 h 27 min
12:45 to 14:28 = 1 h 43 min
12:45 to 14:27 = 1 h 42 min
12:45 to 14:51 = 2 h 6 min
12:54 to 15:13 = 2 h 19 min
13:12 to 15:31 = 2 h 19 min
13:15 to 14:51 = 1 h 36 min
Hence, the 13.15 h is the quickest journey at 1 h 36 min
73
© 2014, John Bird