City Z and City A are 369 km apart. At 6.43 p.m., Liam is travelling at a uniform speed left City Z for City A while Michael set off from City A to City Z along the same road at a uniform speed, which was 9 km/h slower than that of Liam. The two met at 9.43 p.m.
- Find the speed of Liam.
- If Michael 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 Michael to travel from 6.43 p.m. to 9.43 p.m. = 3 h
Average speed of Liam and Michael
= 369 ÷ 3
= 123 km/h
Liam's speed
= (123 + 9) ÷ 2
= 132 ÷ 2
= 66 km/h
(b)
Michael's speed
= 66 - 9
= 57 km/h
Distance that Michael travelled in 3 h
= 3 x 57
= 171 km
Remaining distance that Michael needed to travel
= 369 - 171
= 198 km
Time that Michael needed to reach his destination after the two met
= 198 ÷ 57
= 3
2757 = 3
919 h
Answer(s): (a) 66 km/h; (b) 3
919 h