9.2.4 Speed and Acceleration, PT3 Focus Practice

Question 9:
Mr Wong is going to watch a movie at 2.30 p.m at a cinema that is 60 km away from his house. He leaves at 1.25 p.m and drives at an average speed of 70 km/h for half an hour. If he drives at an average speed of 75 km/h for the remaining journey, will he arrive before the movie starts?

Give your reason with calculation.

Solution: 
$\begin{array}{l}\text{Distance travelled at the first }\frac{1}{2}\text{ hour}\\ =70\times \frac{1}{2}\\ =35\text{ km}\\ \\ \text{Remaining distance}=60\text{ km}-35\text{ km}\\ =25\text{ km}\\ \text{Time taken for the remaining journey}\\ =\frac{25}{75}\\ =\frac{1}{3}\times 60\\ =20\text{ minutes}\\ \\ \text{Mr Wong arrives at}\\ =1.25\text{ p}\text{.m}+30\text{ minutes}+20\text{ minutes}\\ =2.15\text{ p}\text{.m}\\ \\ \text{Yes, he will arrive before 2}\text{.30 p}\text{.m}\\ \end{array}$

Question 10:
Diagram below shows travel information of Jason and Mary from Town A to Town B. Jason drives a lorry while Mary drives a car.

(a) Jason started his journey from Town A at 7.00 a.m.
State the time, Jason reached at Town B.

(b) If both of them reached Town B at the same time, state the time Mary started her journey from Town A.


Solution:
(a)
Total time taken from Town A to Town B
= 3 hours + 1 hour + 2 hours
= 6 hours

Time Jason reached Town B
= 0700 + 0600
= 1300 hours → 1.00 p.m.

(b)
$\begin{array}{l}\text{Speed}=\frac{\text{Distance}}{\text{Time}}\\ \text{Total distance from Town }A\text{ to Town }B\\ =\left(60\times 3\right)+\left(75\times 2\right)\\ =180+150\\ =330\text{ km}\\ \\ \text{Time taken by Mary}\\ =\frac{330}{100}\\ =3.3\text{ hours}\\ =3\text{ hours }18\text{ minutes }\leftarrow \boxed{\begin{array}{l}0.3\times 60\\ =18\text{ minutes}\end{array}}\\ \\ \text{The time Mary started her journey from Town }A=9.42\text{ a}\text{.m}\text{.}\end{array}$