City B and City C are 540 km apart. At 5.57 p.m., Pierre is travelling at a uniform speed left City B for City C while Archie set off from City C to City B along the same road at a uniform speed, which was 5 km/h slower than that of Pierre. The two met at 9.57 p.m.
- Find the speed of Pierre.
- If Archie 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 Archie to travel from 5.57 p.m. to 9.57 p.m. = 4 h
Average speed of Pierre and Archie
= 540 ÷ 4
= 135 km/h
Pierre's speed
= (135 + 5) ÷ 2
= 140 ÷ 2
= 70 km/h
(b)
Archie's speed
= 70 - 5
= 65 km/h
Distance that Archie travelled in 4 h
= 4 x 65
= 260 km
Remaining distance that Archie needed to travel
= 540 - 260
= 280 km
Time that Archie needed to reach his destination after the two met
= 280 ÷ 65
= 4
2065 = 4
413 h
Answer(s): (a) 70 km/h; (b) 4
413 h