City V and City W are 580 km apart. At 3.15 p.m., Liam is travelling at a uniform speed left City V for City W while Tom set off from City W to City V along the same road at a uniform speed, which was 5 km/h slower than that of Liam. The two met at 7.15 p.m.
- Find the speed of Liam.
- If Tom 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 Liam and Tom to travel from 3.15 p.m. to 7.15 p.m. = 4 h
Average speed of Liam and Tom
= 580 ÷ 4
= 145 km/h
Liam's speed
= (145 + 5) ÷ 2
= 150 ÷ 2
= 75 km/h
(b)
Tom's speed
= 75 - 5
= 70 km/h
Distance that Tom travelled in 4 h
= 4 x 70
= 280 km
Remaining distance that Tom needed to travel
= 580 - 280
= 300 km
Time that Tom needed to reach his destination after the two met
= 300 ÷ 70
= 4
2070 = 4
27 h
Answer(s): (a) 75 km/h; (b) 4
27 h