City X and City Y are 540 km apart. At 3.23 p.m., Tim is travelling at a uniform speed left City X for City Y while Wesley set off from City Y to City X along the same road at a uniform speed, which was 10 km/h slower than that of Tim. The two met at 6.23 p.m.
- Find the speed of Tim.
- If Wesley 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 Tim and Wesley to travel from 3.23 p.m. to 6.23 p.m. = 3 h
Average speed of Tim and Wesley
= 540 ÷ 3
= 180 km/h
Tim's speed
= (180 + 10) ÷ 2
= 190 ÷ 2
= 95 km/h
(b)
Wesley's speed
= 95 - 10
= 85 km/h
Distance that Wesley travelled in 3 h
= 3 x 85
= 255 km
Remaining distance that Wesley needed to travel
= 540 - 255
= 285 km
Time that Wesley needed to reach his destination after the two met
= 285 ÷ 85
= 3
3085 = 3
617 h
Answer(s): (a) 95 km/h; (b) 3
617 h