14.2.2 Ratio, Rates and Proportions II, PT3 Focus Practice

Question 6:
Mei Ling drives her car from Kuantan to Kuala Terengganu for a distance of 170 km for 2 hours. She then continues her journey to Kota Bahru and increases her speed to 100 kmh^-1 for 45 minutes.
Calculate the acceleration, in kmh^-2, of the car.

Solution:
$\begin{array}{l}\text{Speed from Kuantan to Kuala Terengganu}\\ =\frac{170}{2}=85{\text{ kmh}}^{-1}\\ \\ \text{Acceleration}\\ =\frac{\text{Final speed}-\text{Initial speed}}{\text{Time taken}}\\ =\frac{100-85}{\frac{45}{60}}\\ =20{\text{ kmh}}^{-2}\end{array}$

Question 7:
Diagram shows the distance between K and L.

A car moves from K to L with an average speed of 80 kmh^-1. After rest for 1 hour 30 minutes, the car then returns to K. The average speed of the car from L to K increases 20%. If the car reaches K at 5 p.m., calculate the time the car starts its journey from K.

Solution: 
$\begin{array}{l}\text{The time taken from }K\text{ to }L\\ =\frac{160}{80}\\ =2\text{ hrs}\\ \\ \text{The average speed from }L\text{ to }K\\ =80\times 1.2\\ =96{\text{ kmh}}^{-1}\\ \\ \text{The time taken from }L\text{ to }K\\ =\frac{160}{96}\\ =1\frac{2}{3}\text{ hrs}\\ \\ \text{The total time taken for the whole journey}\\ =2+1\frac{1}{2}+1\frac{2}{3}\\ =5\frac{1}{6}\text{ hrs}\\ =5\text{ hour }10\text{ minutes}\end{array}$



The car starts its journey from K at 11:50 a.m.

Question 8:
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 9:
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:
$\begin{array}{l}\text{From }P\text{ to }Q\text{:}\\ \text{Average speed}=80\text{ km/h}\\ \text{Time taken = 2 hours 15 minutes}\\ \text{ = 2}\frac{1}{4}\text{ hours}\\ \text{Distance}=\text{average speed}\times \text{time taken}\\ \text{Distance }=80\times 2\frac{1}{4}\\ =80\times \frac{9}{4}\\ =180\text{ km}\\ \\ \text{From }Q\text{ to }R\text{:}\\ \text{Distance }=90\text{ km}\\ \text{Time taken = 45 minutes}\\ \text{ = }\frac{3}{4}\text{ hour}\\ \\ \text{Average speed from }P\text{ to }R\\ =\frac{180+90}{2\frac{1}{4}+\frac{3}{4}}\leftarrow \boxed{\frac{\text{Total distance}}{\text{Total time}}}\\ =\frac{270}{3}\\ =90\text{ km/h}\end{array}$