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:
Speed from Kuantan to Kuala Terengganu = 170 2 =85  kmh 1 Acceleration = Final speedInitial speed Time taken = 10085 45 60 =20  kmh 2


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
The time taken from K to L = 160 80 =2 hrs The average speed from L to K =80×1.2 =96  kmh 1 The time taken from L to K = 160 96 =1 2 3  hrs The total time taken for the whole journey =2+1 1 2 +1 2 3 =5 1 6  hrs =5 hour 10 minutes



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
Distance travelled at the first  1 2  hour =70× 1 2 =35 km Remaining distance=60 km35 km    =25 km Time taken for the remaining journey = 25 75 = 1 3 ×60 =20 minutes Mr Wong arrives at =1.25 p.m+30 minutes+20 minutes =2.15 p.m Yes, he will arrive before 2.30 p.m


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:
From P to Q: Average speed=80 km/h Time taken = 2 hours 15 minutes                    = 2 1 4  hours Distance=average speed×time taken Distance =80×2 1 4                =80× 9 4                =180 km From Q to R: Distance =90 km Time taken = 45 minutes                    =  3 4  hour Average speed from P to R = 180+90 2 1 4 + 3 4 Total distance Total time = 270 3 =90 km/h

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