GOING MY WAY EXAMPLES
When an object moves at a “constant” speed, or rate, it is said to be in “uniform
motion.” The formula “d = rt” is used to solve uniform motion problems. In the formula,
“d” represents distance, “r” represents rate, and “t” represents time.
In the formula, “r” can represent an
“average” rate instead of a “constant”
rate.
Example # 1 Î Joe rides his bicycle at a speed of 8 mph (miles per hour). How long will
it take him to ride 28 miles?
Explore ÎLet “t” = the time it takes Joe to ride 28 miles.
Plan Î d = rt
28 = 8t
Solve Î d = rt
28 = 8t
1
3
=t
2
Joe will take 3
1
hours to ride 28 miles.
2
Examine Î28 = (3
1
)(8)
2
28 = 28
Johnny Wolfe
Jay High School
Santa Rosa County Florida
August 2, 2001
Discussion question # 1 Î If Sue doubles her speed and doubles the distance traveled,
what effect does this have on the time needed? (Remains the same)
Example # 2 Î Doug and Wanda leave their home in Chattanooga at the same time.
They travel in opposite directions. Doug travels at 80 km/h (kilometers per hour) and
Wanda travels 72 kh/h. In how many hours will they be 760 km apart?
760 km
Doug
Wanda
80 km/k
72 km/k
Explore ÎLet “t” = represent the number of hours.
Plan
r(t) = d
Doug
Wanda
80
72
t
t
Doug travels 80t km.
80t
72t
Wanda travels 72t km.
They travel a total of 760 km.
Doug’s distance + Wanda’s distance = total distance
80t + 72t = 760
Solve Î 80t + 72t = 760
152t = 760
t=5
In 5 hours, Doug and Wanda will be 760 km apart.
Examine Î80(5) + 72(5) = 760
400 + 360 = 760
760 = 760
Johnny Wolfe
Jay High School
Santa Rosa County Florida
August 2, 2001
Example # 3 ÎSuppose Dan and Donna leave at the same time traveling the same
direction. Dan drives 70 km/h, Donna drives 85 km/h. How long until they are 90 km
apart?
D1 = 85(t)
Donna
Dan
D2 = 70(t)
90 km
Explore ÎLet “t” = represent the number of hours.
Plan
85t – 70t = 90
Dan
Donna
70
85
t
t
Doug travels 70t km.
70t
85t
Wanda travels 85t km.
The distance between what Donna drives and what Dan drives is 90 km.
Donna’s distance – Doug’s distance = 90 km.
85t – 70t = 90
Solve Î 85t – 70t = 90
15t = 90
t=6
In 6 hours, Donna and Dan will be 90 km apart.
Examine Î 85(6) – 70(6) = 90
510 – 420 = 90
90 = 90
Johnny Wolfe
Jay High School
Santa Rosa County Florida
August 2, 2001
Example # 4 ÎAt 8:00 A.M. Peggy leaves home driving 35 mph. A half hour later,
Doug discovers that she left her briefcase. He drives 50 mph to catch up
with her. If Doug is delayed 15 minutes with a flat tire, at what time will
he catch up to Peggy?
Explore ÎLet “x” = the time Peggy travels until Doug arrives.
Plan
r(t) = d
Peggy
Doug
35
50
x
x-
Peggy travels 35x mi.
35x
3
4
50(x -
3
)
4
Doug travels (50x – 37.5 mi.
Peggy and Doug travel the same distance.
35x = 50x – 37.5
Solve Î 35x = 50x – 37.5
-15x = -37.5
x = 2.5
1
hours when Doug catches up to her.
2
1
Doug catches up to Peggy at 8 A.M. + 2
hours or 10:30 A.M.
2
Peggy has been traveling for 2
Examine Î 35(2.5) = 50(2.5) – 37.5
87.5 = 125 – 37.5
87.5 = 87.5
Johnny Wolfe
Jay High School
Santa Rosa County Florida
August 2, 2001
Name:________________
Date:____________
Class:____________
GOING MY WAY WORKSHEET
Use the 4-step approach to problem solving:
1.
2.
3.
4.
Explore “Define a variable”
Plan “Write an equation”
Solve “Solve the equation and answer the problem”
Examine “Check to see if the answer makes sense”
1. Pat is driving 80 km/h. How far will she travel in 2 hours?
2. Marilyn traveled 240 miles. What was her rate if she made the trip in 6 hours?
3. Rudy rode his bicycle 72 km. How long did it take him if his rate was 9 km/h?
4. Two trains lave Bridgeport at the same time, one traveling north, the other south.
The first train travels at 40 mph and the second at 30 mph. In how many hours
will the trains be 245 miles apart?
5. Two cyclists are traveling in the same direction on the same course. One travels
20 mph and the other 14 mph. After how many hours will they be 15 miles apart?
6. An express train travels 80 km/h from Wheaton to Whitfield. A passenger train,
traveling 48 kh/h, takes 2 hours longer for the same trip. If the time for the
express train is x hours, how far apart are Wheaton and Whitfield?
7. At 1:30 P.M., a plane leaves Tucson for Baltimore, a distance of 2240 miles. The
plane flies 280 mph. A second plane leaves Tucson at 2:15 P.M., and is scheduled
to land in Baltimore 15 minutes before the first plane. At what rate must the
second plane travel to arrive on schedule?
Johnny Wolfe
Jay High School
Santa Rosa County Florida
August 2, 2001
GOING MY WAY WORKSHEET KEY
Use the 4-step approach to problem solving:
a.
b.
c.
d.
Explore “Define a variable”
Plan “Write an equation”
Solve “Solve the equation and answer the problem”
Examine “Check to see if the answer makes sense”
1. Pat is driving 80 km/h. How far will she travel in 2 hours?
Explore ÎLet “d” = distance Pat can travel in 2 hours.
Plan Î d = rt
d = (80)(2)
Solve Î d = rt
d = (80)(2)
d = 160
Pat will travel 160 km in 2 hours.
Examine Î160 = (80)(2)
160 = 160
Johnny Wolfe
Jay High School
Santa Rosa County Florida
August 2, 2001
2. Marilyn traveled 240 miles. What was her rate if she made the trip in 6 hours?
Explore ÎLet “r” = rate Marilyn travels.
Plan Î d = rt
240 = r(6)
Solve Î d = rt
240 = 6r
40 = r
Marilyn will travel 40 mph.
Examine Î240 = 40(6)
240 = 240
3. Rudy rode his bicycle 72 km. how long did it take him if his rate was 9 km/h?
Explore ÎLet “t” = time is too Rudy to ride 72 km.
Plan Î d = rt
72 = 9(t)
Solve Î d = rt
72 = 9t
8=t
It will take Rudy 8 hours to go 72 km.
Examine Î 72 = 9(8)
72 = 72
Johnny Wolfe
Jay High School
Santa Rosa County Florida
August 2, 2001
4. Two trains lave Bridgeport at the same time, one traveling north, the other
south. The first train travels at 40 mph and the second at 30 mph. In how
many hours will the trains be 245 miles apart?
Explore ÎLet “t” = time the two trains were traveling.
Plan Î d = rt
d1 = (40)t
d2 = (30)t
The total distance the train covered is 245 miles.
d1 + d2 = Total distance
40t + 30t = 245
Solve Î 40t + 30t = 245
70t = 245
t = 3.5
In 3
1
hours the two trains will be 245 miles apart.
2
1
Examine Î70( 3 ) = 245
2
245 = 245
Johnny Wolfe
Jay High School
Santa Rosa County Florida
August 2, 2001
5. Two cyclists are traveling in the same direction on the same course. One
travels 20 mph and the other 14 mph. After how many hours will they be 15
miles apart?
Explore ÎLet “t” = time the two cyclists were on the road.
Plan Î d = rt
d1 = (20)t
d2 = (14)t
The difference between the two cyclists is 15 miles.
d1 - d2 = distance apart
20t – 14t = 15
Solve Î 20t – 14t = 15
6t = 15
t = 2.5
1
hours the first cyclist will lead the second cyclist
2
by 15 miles.
In 2
Examine Î20(2.5) – 14(2.5) = 15
50 – 35 = 15
15 = 15
Johnny Wolfe
Jay High School
Santa Rosa County Florida
August 2, 2001
8. An express train travels 80 km/h from Wheaton to Whitfield. A passenger train,
traveling 48 kh/h, takes 2 hours longer for the same trip. If the time for the
express train is x hours, how far apart are Wheaton and Whitfield?
Explore ÎLet “ x ” = time the express train is traveling.
Let (x x + 2) = time passenger train is traveling.
Plan Î d = rt
d1 = (80)( x )
d2 = (48)( x + 2)
Distance both trains travel are equal.
d1 = d2
80 x = 48( x + 2)
Solve Î 80 x = 48( x + 2)
80 x = 48 x + 96
32 x = 96
x = 3 Îx = 9
It takes the express train 9 hours to make the trip.
d = (80) 9
d = 240 km
Examine Î80( 9 ) = 48( 9 + 2)
240 = 48(5)
240 = 240
Johnny Wolfe
Jay High School
Santa Rosa County Florida
August 2, 2001
6. At 1:30 P.M., a plane leaves Tucson for Baltimore, a distance of 2240 miles.
The plane flies 280 mph. A second plane leaves Tucson at 2:15 P.M., and is
scheduled to land in Baltimore 15 minutes before the first plane. At what rate
must the second plane travel to arrive on schedule?
Plan Î d = rt Let x = time first plane leaves Tucson.
Second plane leaves 45 minutes later and lands 15 minutes
earlier. Therefore, plane two is in the air 1 hour less (x – 1).
Plane 1 Î2240 = 280(x)
Plane 2 Î2240 = r(x – 1)
Distances both planes travel are equal.
Solve Î Plane 1 Î2240 = 280x
x = 8 hours for plane 1
Plane 2 Î2240 = r(8 – 1)
2240 = 7r
320 = r
Plane 2 travels 320 miles per hour.
Examine Î2240 = (320)(8 – 1)
2240 = (320)(7)
2240 = 2240
Johnny Wolfe
Jay High School
Santa Rosa County Florida
August 2, 2001
Student Name: __________________
Date: ______________
GOING MY WAY CHECKLIST
1. On each problem, did the student diagram and label problem correctly?
a.
b.
c.
d.
e.
f.
All seven (30 points)
Six of the seven (25 points)
Five of the seven (20 points)
Four of the seven (15 points)
Three of the seven (10 points)
Two of the seven (5 points)
2. On each problem, did the student use the 4-step approach to problem solving?
a.
b.
c.
d.
e.
f.
All seven (30 points)
Six of the seven (25 points)
Five of the seven (20 points)
Four of the seven (15 points)
Three of the seven (10 points)
Two of the seven (5 points)
3. On each problem, did the student solve the problem correctly?
a.
b.
c.
d.
e.
f.
All seven (30 points)
Six of the seven (25 points)
Five of the seven (20 points)
Four of the seven (15 points)
Three of the seven (10 points)
Two of the seven (5 points)
Total Number of Points _________
A
81 points and above
B
72 points and above
C
63 points and above
D
54 points and above
F
53 points and
Johnny Wolfe
Jay High School
Any score below C
needs
remediation!
Santa Rosa County Florida
August 2, 2001