City H and City J are 360 km apart. At 1.35 p.m., Ryan is travelling at a uniform speed left City H for City J while Howard set off from City J to City H along the same road at a uniform speed, which was 12 km/h slower than that of Ryan. The two met at 4.35 p.m.
- Find the speed of Ryan.
- 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 Ryan and Howard to travel from 1.35 p.m. to 4.35 p.m. = 3 h
Average speed of Ryan and Howard
= 360 ÷ 3
= 120 km/h
Ryan's speed
= (120 + 12) ÷ 2
= 132 ÷ 2
= 66 km/h
(b)
Howard's speed
= 66 - 12
= 54 km/h
Distance that Howard travelled in 3 h
= 3 x 54
= 162 km
Remaining distance that Howard needed to travel
= 360 - 162
= 198 km
Time that Howard needed to reach his destination after the two met
= 198 ÷ 54
= 3
3654 = 3
23 h
Answer(s): (a) 66 km/h; (b) 3
23 h