City U and City V are 564 km apart. At 3.17 p.m., Paul is travelling at a uniform speed left City U for City V while Ethan set off from City V to City U along the same road at a uniform speed, which was 9 km/h slower than that of Paul. The two met at 7.17 p.m.
- Find the speed of Paul.
- If Ethan 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 Ethan to travel from 3.17 p.m. to 7.17 p.m. = 4 h
Average speed of Paul and Ethan
= 564 ÷ 4
= 141 km/h
Paul's speed
= (141 + 9) ÷ 2
= 150 ÷ 2
= 75 km/h
(b)
Ethan's speed
= 75 - 9
= 66 km/h
Distance that Ethan travelled in 4 h
= 4 x 66
= 264 km
Remaining distance that Ethan needed to travel
= 564 - 264
= 300 km
Time that Ethan needed to reach his destination after the two met
= 300 ÷ 66
= 4
3666 = 4
611 h
Answer(s): (a) 75 km/h; (b) 4
611 h