City C and City D are 465 km apart. At 5.11 p.m., Liam is travelling at a uniform speed left City C for City D while Ken set off from City D to City C along the same road at a uniform speed, which was 5 km/h slower than that of Liam. The two met at 8.11 p.m.
- Find the speed of Liam.
- If Ken 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 Ken to travel from 5.11 p.m. to 8.11 p.m. = 3 h
Average speed of Liam and Ken
= 465 ÷ 3
= 155 km/h
Liam's speed
= (155 + 5) ÷ 2
= 160 ÷ 2
= 80 km/h
(b)
Ken's speed
= 80 - 5
= 75 km/h
Distance that Ken travelled in 3 h
= 3 x 75
= 225 km
Remaining distance that Ken needed to travel
= 465 - 225
= 240 km
Time that Ken needed to reach his destination after the two met
= 240 ÷ 75
= 3
1575 = 3
15 h
Answer(s): (a) 80 km/h; (b) 3
15 h