City W and City X are 456 km apart. At 2.11 p.m., Liam is travelling at a uniform speed left City W for City X while Ryan set off from City X to City W along the same road at a uniform speed, which was 8 km/h slower than that of Liam. The two met at 5.11 p.m.
- Find the speed of Liam.
- If Ryan 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 Ryan to travel from 2.11 p.m. to 5.11 p.m. = 3 h
Average speed of Liam and Ryan
= 456 ÷ 3
= 152 km/h
Liam's speed
= (152 + 8) ÷ 2
= 160 ÷ 2
= 80 km/h
(b)
Ryan's speed
= 80 - 8
= 72 km/h
Distance that Ryan travelled in 3 h
= 3 x 72
= 216 km
Remaining distance that Ryan needed to travel
= 456 - 216
= 240 km
Time that Ryan needed to reach his destination after the two met
= 240 ÷ 72
= 3
2472 = 3
13 h
Answer(s): (a) 80 km/h; (b) 3
13 h