City H and City J are 414 km apart. At 3.58 p.m., Howard is travelling at a uniform speed left City H for City J while Luke set off from City J to City H along the same road at a uniform speed, which was 6 km/h slower than that of Howard. The two met at 6.58 p.m.
- Find the speed of Howard.
- If Luke 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 Luke to travel from 3.58 p.m. to 6.58 p.m. = 3 h
Average speed of Howard and Luke
= 414 ÷ 3
= 138 km/h
Howard's speed
= (138 + 6) ÷ 2
= 144 ÷ 2
= 72 km/h
(b)
Luke's speed
= 72 - 6
= 66 km/h
Distance that Luke travelled in 3 h
= 3 x 66
= 198 km
Remaining distance that Luke needed to travel
= 414 - 198
= 216 km
Time that Luke needed to reach his destination after the two met
= 216 ÷ 66
= 3
1866 = 3
311 h
Answer(s): (a) 72 km/h; (b) 3
311 h