City M and City N are 600 km apart. At 2.40 p.m., Jack is travelling at a uniform speed left City M for City N while Pierre set off from City N to City M along the same road at a uniform speed, which was 10 km/h slower than that of Jack. The two met at 5.40 p.m.
- Find the speed of Jack.
- If Pierre 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 Jack and Pierre to travel from 2.40 p.m. to 5.40 p.m. = 3 h
Average speed of Jack and Pierre
= 600 ÷ 3
= 200 km/h
Jack's speed
= (200 + 10) ÷ 2
= 210 ÷ 2
= 105 km/h
(b)
Pierre's speed
= 105 - 10
= 95 km/h
Distance that Pierre travelled in 3 h
= 3 x 95
= 285 km
Remaining distance that Pierre needed to travel
= 600 - 285
= 315 km
Time that Pierre needed to reach his destination after the two met
= 315 ÷ 95
= 3
3095 = 3
619 h
Answer(s): (a) 105 km/h; (b) 3
619 h