City G and City H are 402 km apart. At 2.50 p.m., Howard is travelling at a uniform speed left City G for City H while Charlie set off from City H to City G along the same road at a uniform speed, which was 8 km/h slower than that of Howard. The two met at 5.50 p.m.
- Find the speed of Howard.
- If Charlie 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 Howard and Charlie to travel from 2.50 p.m. to 5.50 p.m. = 3 h
Average speed of Howard and Charlie
= 402 ÷ 3
= 134 km/h
Howard's speed
= (134 + 8) ÷ 2
= 142 ÷ 2
= 71 km/h
(b)
Charlie's speed
= 71 - 8
= 63 km/h
Distance that Charlie travelled in 3 h
= 3 x 63
= 189 km
Remaining distance that Charlie needed to travel
= 402 - 189
= 213 km
Time that Charlie needed to reach his destination after the two met
= 213 ÷ 63
= 3
2463 = 3
821 h
Answer(s): (a) 71 km/h; (b) 3
821 h