City M and City N are 396 km apart. At 6.46 p.m., Warren is travelling at a uniform speed left City M for City N while Howard set off from City N to City M along the same road at a uniform speed, which was 6 km/h slower than that of Warren. The two met at 9.46 p.m.
- Find the speed of Warren.
- 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 Warren and Howard to travel from 6.46 p.m. to 9.46 p.m. = 3 h
Average speed of Warren and Howard
= 396 ÷ 3
= 132 km/h
Warren's speed
= (132 + 6) ÷ 2
= 138 ÷ 2
= 69 km/h
(b)
Howard's speed
= 69 - 6
= 63 km/h
Distance that Howard travelled in 3 h
= 3 x 63
= 189 km
Remaining distance that Howard needed to travel
= 396 - 189
= 207 km
Time that Howard needed to reach his destination after the two met
= 207 ÷ 63
= 3
1863 = 3
27 h
Answer(s): (a) 69 km/h; (b) 3
27 h