City V and City W are 360 km apart. At 2.30 p.m., Luke is travelling at a uniform speed left City V for City W while Fred set off from City W to City V along the same road at a uniform speed, which was 8 km/h slower than that of Luke. The two met at 5.30 p.m.
- Find the speed of Luke.
- If Fred 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 Luke and Fred to travel from 2.30 p.m. to 5.30 p.m. = 3 h
Average speed of Luke and Fred
= 360 ÷ 3
= 120 km/h
Luke's speed
= (120 + 8) ÷ 2
= 128 ÷ 2
= 64 km/h
(b)
Fred's speed
= 64 - 8
= 56 km/h
Distance that Fred travelled in 3 h
= 3 x 56
= 168 km
Remaining distance that Fred needed to travel
= 360 - 168
= 192 km
Time that Fred needed to reach his destination after the two met
= 192 ÷ 56
= 3
2456 = 3
37 h
Answer(s): (a) 64 km/h; (b) 3
37 h