City A and City B are 405 km apart. At 1.43 p.m., Pierre is travelling at a uniform speed left City A for City B while Ben set off from City B to City A along the same road at a uniform speed, which was 9 km/h slower than that of Pierre. The two met at 4.43 p.m.
- Find the speed of Pierre.
- If Ben 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 Pierre and Ben to travel from 1.43 p.m. to 4.43 p.m. = 3 h
Average speed of Pierre and Ben
= 405 ÷ 3
= 135 km/h
Pierre's speed
= (135 + 9) ÷ 2
= 144 ÷ 2
= 72 km/h
(b)
Ben's speed
= 72 - 9
= 63 km/h
Distance that Ben travelled in 3 h
= 3 x 63
= 189 km
Remaining distance that Ben needed to travel
= 405 - 189
= 216 km
Time that Ben needed to reach his destination after the two met
= 216 ÷ 63
= 3
2763 = 3
37 h
Answer(s): (a) 72 km/h; (b) 3
37 h