14.2.1 Ratio, Rates and Proportions II, PT3 Focus Practice

Question 1:
The distance from town A to town B is 120 km. A car leaves town A for town B at 11.00 a.m. The average speed is 80 km h^-1 .
At what time does the car arrive at town B.

Solution:
$\begin{array}{l}\text{Time taken}=\frac{\text{distance travelled}}{\text{average speed}}\\ =\frac{120\text{ km}}{80{\text{ km h}}^{-1}}\\ =\frac{3}{2}\text{ hours}\\ \text{= 1 hour 30 minutes}\\ \text{1 hour 30 minutes after 11}\text{.00 a}\text{.m}\text{. is 12}\text{.30 p}\text{.m}\text{.}\end{array}$

Question 2:
Kenny drives his car from town P to town Q at a distance of 180 km in 3 hours.
Faisal takes 30 minutes less than Kenny for the same journey.
Calculate the average speed, in km/h, of Faisal’s car.

Solution:
$\begin{array}{l}\text{Time taken by Faisal}\\ \text{= 3 hours}-30\text{ minutes}\\ \text{= 3 hours}-\frac{1}{2}\text{ hour}\\ \text{= 2}\frac{1}{2}\text{ hours}\\ \\ \text{Average speed of Faisal's car}\\ =\frac{\text{distance travelled}}{\text{time taken}}\\ =\frac{180\text{ km}}{\text{2}\frac{1}{2}\text{ hours}}\\ =72\text{ km/h}\end{array}$

Question 3:
Rafidah drives her car from town L to town M at an average speed of 90 km/h for 2 hours 40 minutes. She continues her journey for a distance of 100 km from town M to town N and takes 1 hour 20 minutes.
Calculate the average speed, in km/h, for the journey from L to M.

Solution:
$\begin{array}{l}\text{Distance}=\text{average speed}\times \text{time taken}\\ \text{Distance from }L\text{ to }M=90\times 2\frac{40}{60}\\ =90\times 2\frac{2}{3}\\ =90\times \frac{8}{3}\\ =240\text{ km}\\ \\ \text{Total distance from }L\text{ to }N=240+100\\ =340\text{ km}\\ \\ \text{Total time taken = 2 hours 40 minutes + 1 hour 20 minutes}\\ \text{ = 4 hours}\\ \text{Average speed for the journey from }L\text{ to }N=\frac{340\text{ km}}{4\text{ h}}\\ =85\text{ km/h}\end{array}$

Question 4:
Susan drives at an average speed of 105 km/h from town F to town G.
The journey takes 3 hours.
Susan takes 30 minutes longer for her return journey from town G to town F. Calculate the average speed, in km/h, for the return journey.

Solution:
$\begin{array}{l}\text{Distance from }F\text{ to }G\\ \text{= 105 km/h}\times \text{3 hours}\\ \text{=315 km}\\ \\ \text{Average speed for return journey}\\ =\frac{\text{distance travelled}}{\text{time taken}}\\ =\frac{315\text{ km}}{3\frac{1}{2}\text{ hours}}\\ =90\text{ km/h}\end{array}$

Question 5:
Table below shows the distances travelled and the average speeds for four vehicles.

Vehicle	Distance (km)	Average speed (km/h)
A	230	115
B	250	100
C	170	85
D	245	70

Which vehicles took the same time to complete the journey?

Solution:
$\begin{array}{l}\text{Time taken for vehicle }A=\frac{230}{115}=2\text{ hours}\\ \text{Time taken for vehicle }B=\frac{250}{100}=2\frac{1}{2}\text{ hours}\\ \text{Time taken for vehicle }C=\frac{170}{85}=2\text{ hours}\\ \text{Time taken for vehicle }D=\frac{245}{60}=3\frac{1}{2}\text{ hours}\end{array}$

Thus, the vehicles A and C took the same time to complete the journey.