City A and City B are 340 km apart. At 5.17 p.m., Liam is travelling at a uniform speed left City A for City B while Paul set off from City B to City A along the same road at a uniform speed, which was 10 km/h slower than that of Liam. The two met at 7.17 p.m.
- Find the speed of Liam.
- If Paul 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 Paul to travel from 5.17 p.m. to 7.17 p.m. = 2 h
Average speed of Liam and Paul
= 340 ÷ 2
= 170 km/h
Liam's speed
= (170 + 10) ÷ 2
= 180 ÷ 2
= 90 km/h
(b)
Paul's speed
= 90 - 10
= 80 km/h
Distance that Paul travelled in 2 h
= 2 x 80
= 160 km
Remaining distance that Paul needed to travel
= 340 - 160
= 180 km
Time that Paul needed to reach his destination after the two met
= 180 ÷ 80
= 2
2080 = 2
14 h
Answer(s): (a) 90 km/h; (b) 2
14 h