**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*:$\begin{array}{l}\text{From}P\text{to}Q\text{:}\\ \text{Averagespeed}=80\text{km/h}\\ \text{Timetaken=2hours15minutes}\\ \text{=2}\frac{1}{4}\text{hours}\\ \text{Distance}=\text{averagespeed}\times \text{timetaken}\\ \text{Distance}=80\times 2\frac{1}{4}\\ \text{}=80\times \frac{9}{4}\\ \text{}=180\text{km}\\ \\ \text{From}Q\text{to}R\text{:}\\ \text{Distance}=90\text{km}\\ \text{Timetaken=45minutes}\\ \text{=}\frac{3}{4}\text{hour}\\ \\ \text{Averagespeedfrom}P\text{to}R\\ =\frac{180+90}{2\frac{1}{4}+\frac{3}{4}}\leftarrow \overline{)\frac{\text{Totaldistance}}{\text{Totaltime}}}\\ =\frac{270}{3}\\ =90\text{km/h}\end{array}$

**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)**

$\begin{array}{l}\text{ThespeedofthebicyclefromTown}P\text{toTown}Q\\ =\frac{\text{Distance}}{\text{Time}}\\ =\frac{10}{2}\\ =5\text{km/h}\end{array}$

**(b)**

$\begin{array}{l}\text{Speed}=\frac{\text{Distance}}{\text{Time}}\\ \\ \text{Rahimtook30minutesrestatTown}Q\text{.}\\ \text{TimetakenwhenhisjourneytoTown}R\text{threetimes}\\ \text{fasterthanhisearlierspeed}\text{.}\\ =\frac{25}{5\times 3}\\ =\frac{5}{3}\\ =1\frac{2}{3}\text{hours}\\ =1\text{hour40minutes}\leftarrow \overline{)\begin{array}{l}\frac{2}{3}\times 60\\ =40\text{minutes}\end{array}}\\ \\ \text{TotaltimetakenfromTown}P\text{toTown}Q\text{andTown}Q\text{toTown}R\\ =2\text{hours}+30\text{minutes}+1\text{hour40minutes}\\ =4\text{hour10minutes}\\ \\ \text{ThetimehereachedTown}R\text{at1}\text{.10p}\text{.m}\text{.}\end{array}$