9.2.3 Speed and Acceleration, PT3 Focus Practice

Question 7:
Karen drives her car from town P to town Q at an average speed of 80 km/h for 2 hours 15 minutes. She continues her journey for a distance of 90 km from town Q to town R and takes 45 minutes.
Calculate the average speed, in km/h, for the journey from P to R.

Solution:
$\begin{array}{l}\text{From }P\text{ to }Q\text{:}\\ \text{Average speed}=80\text{ km/h}\\ \text{Time taken = 2 hours 15 minutes}\\ \text{ = 2}\frac{1}{4}\text{ hours}\\ \text{Distance}=\text{average speed}\times \text{time taken}\\ \text{Distance }=80\times 2\frac{1}{4}\\ =80\times \frac{9}{4}\\ =180\text{ km}\\ \\ \text{From }Q\text{ to }R\text{:}\\ \text{Distance }=90\text{ km}\\ \text{Time taken = 45 minutes}\\ \text{ = }\frac{3}{4}\text{ hour}\\ \\ \text{Average speed from }P\text{ to }R\\ =\frac{180+90}{2\frac{1}{4}+\frac{3}{4}}\leftarrow \boxed{\frac{\text{Total distance}}{\text{Total time}}}\\ =\frac{270}{3}\\ =90\text{ km/h}\end{array}$

Question 8:
Diagram below shows the distance from Town P to Town Q and Town Q to Town R.
(a) Rahim rode his bicycle from Town P at 9.00 a.m. and took 2 hours to reach Town Q.
What is the speed, in km/h, of the bicycle?

(b) Rahim took 30 minutes rest at Town Q and continued his journey to Town R three times faster than his earlier speed.
State the time he reached Town R.


Solution:
(a)
$\begin{array}{l}\text{The speed of the bicycle from Town }P\text{ to Town }Q\\ =\frac{\text{Distance}}{\text{Time}}\\ =\frac{10}{2}\\ =5\text{ km/h}\end{array}$

(b)
$\begin{array}{l}\text{Speed}=\frac{\text{Distance}}{\text{Time}}\\ \\ \text{Rahim took 30 minutes rest at Town }Q\text{.}\\ \text{Time taken when his journey to Town }R\text{ three times}\\ \text{faster than his earlier speed}\text{.}\\ =\frac{25}{5\times 3}\\ =\frac{5}{3}\\ =1\frac{2}{3}\text{ hours}\\ =1\text{ hour 40 minutes }\leftarrow \boxed{\begin{array}{l}\frac{2}{3}\times 60\\ =40\text{ minutes}\end{array}}\\ \\ \text{Total time taken from Town }P\text{ to Town }Q\text{ and Town }Q\text{ to Town }R\\ =2\text{ hours }+30\text{ minutes}+1\text{ hour 40 minutes}\\ =4\text{ hour 10 minutes}\\ \\ \text{The time he reached Town }R\text{ at 1}\text{.10 p}\text{.m}\text{.}\end{array}$