City W and City X are 592 km apart. At 4.42 p.m., Jack is travelling at a uniform speed left City W for City X while Howard set off from City X to City W along the same road at a uniform speed, which was 12 km/h slower than that of Jack. The two met at 8.42 p.m.
- Find the speed of Jack.
- If Howard 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 Howard to travel from 4.42 p.m. to 8.42 p.m. = 4 h
Average speed of Jack and Howard
= 592 ÷ 4
= 148 km/h
Jack's speed
= (148 + 12) ÷ 2
= 160 ÷ 2
= 80 km/h
(b)
Howard's speed
= 80 - 12
= 68 km/h
Distance that Howard travelled in 4 h
= 4 x 68
= 272 km
Remaining distance that Howard needed to travel
= 592 - 272
= 320 km
Time that Howard needed to reach his destination after the two met
= 320 ÷ 68
= 4
4868 = 4
1217 h
Answer(s): (a) 80 km/h; (b) 4
1217 h