City W and City X are 540 km apart. At 1.45 p.m., Paul is travelling at a uniform speed left City W for City X while Daniel set off from City X to City W along the same road at a uniform speed, which was 5 km/h slower than that of Paul. The two met at 5.45 p.m.
- Find the speed of Paul.
- If Daniel 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 Paul and Daniel to travel from 1.45 p.m. to 5.45 p.m. = 4 h
Average speed of Paul and Daniel
= 540 ÷ 4
= 135 km/h
Paul's speed
= (135 + 5) ÷ 2
= 140 ÷ 2
= 70 km/h
(b)
Daniel's speed
= 70 - 5
= 65 km/h
Distance that Daniel travelled in 4 h
= 4 x 65
= 260 km
Remaining distance that Daniel needed to travel
= 540 - 260
= 280 km
Time that Daniel 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