City K and City L are 435 km apart. At 1.50 p.m., Mark is travelling at a uniform speed left City K for City L while Billy set off from City L to City K along the same road at a uniform speed, which was 5 km/h slower than that of Mark. The two met at 4.50 p.m.
- Find the speed of Mark.
- If Billy 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 Mark and Billy to travel from 1.50 p.m. to 4.50 p.m. = 3 h
Average speed of Mark and Billy
= 435 ÷ 3
= 145 km/h
Mark's speed
= (145 + 5) ÷ 2
= 150 ÷ 2
= 75 km/h
(b)
Billy's speed
= 75 - 5
= 70 km/h
Distance that Billy travelled in 3 h
= 3 x 70
= 210 km
Remaining distance that Billy needed to travel
= 435 - 210
= 225 km
Time that Billy needed to reach his destination after the two met
= 225 ÷ 70
= 3
1570 = 3
314 h
Answer(s): (a) 75 km/h; (b) 3
314 h