City U and City V are 320 km apart. At 6.45 p.m., Nick is travelling at a uniform speed left City U for City V while Rael set off from City V to City U along the same road at a uniform speed, which was 10 km/h slower than that of Nick. The two met at 8.45 p.m.
- Find the speed of Nick.
- If Rael continued to travel at the same speed, how long would it take for him to reach his destination after the two met? Express your answer in mixed number.
(a)
Time taken for Nick and Rael to travel from 6.45 p.m. to 8.45 p.m. = 2 h
Average speed of Nick and Rael
= 320 ÷ 2
= 160 km/h
Nick's speed
= (160 + 10) ÷ 2
= 170 ÷ 2
= 85 km/h
(b)
Rael's speed
= 85 - 10
= 75 km/h
Distance that Rael travelled in 2 h
= 2 x 75
= 150 km
Remaining distance that Rael needed to travel
= 320 - 150
= 170 km
Time that Rael needed to reach his destination after the two met
= 170 ÷ 75
= 2
2075 = 2
415 h
Answer(s): (a) 85 km/h; (b) 2
415 h