Tomorrow When The War Began Solution Question 1 Calculate the maximum period of time they can stay at the house, using the formula: #
1– 0.07
If they can accept a 40% chance of being caught, that means a 60% chance of being safe: 0.6
1– 0.07
#
#
This equation can be solved by using logarithms. First we can take the log of both sides: 0.6
1– 0.07
0.6 0.6 #
#
1– 0.07
#
1– 0.07 0.6 /
1– 0.07 #
7.04 (1 mark) The teens shouldn’t spend more than 7 nights at the house before switching to a different property. Question 2 First use the distance formula: 60
60
/ / 0.85
… 1
1
60
/
1
0.85
0.85
In 1 minute travelling at 60 km/hr, the truck will travel 1 km: 1
0.85
1
0.85
0.85
1
… (1 mark) We have a geometric series, because each subsequent term is the result of multiplying the previous term by a constant amount – in this case by 0.85. The formula of the sum of a geometric series is: 1
1
where n is the number of terms in the series, and r is the ratio by which each term is multiplied to get the next one, and a is the value of the first term. So this formula looks like this: All material copyright Math Thrills Pty Ltd www.MathThrills.com 1–0.85 1 0.85
1
6.66
6
6.66
(1 mark) The truck will hold out just long enough to make it to safety. Question 3 We can calculate the time to escape using the distance‐speed formula: /
500/10 50
60
/ (1 mark) The fuse burns at 60 cm/s:
3000
50 30 (1 mark) All material copyright Math Thrills Pty Ltd www.MathThrills.com