City W and City X are 504 km apart. At 1.53 p.m., Michael is travelling at a uniform speed left City W for City X while Oscar set off from City X to City W along the same road at a uniform speed, which was 8 km/h slower than that of Michael. The two met at 4.53 p.m.
- Find the speed of Michael.
- If Oscar 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 Michael and Oscar to travel from 1.53 p.m. to 4.53 p.m. = 3 h
Average speed of Michael and Oscar
= 504 ÷ 3
= 168 km/h
Michael's speed
= (168 + 8) ÷ 2
= 176 ÷ 2
= 88 km/h
(b)
Oscar's speed
= 88 - 8
= 80 km/h
Distance that Oscar travelled in 3 h
= 3 x 80
= 240 km
Remaining distance that Oscar needed to travel
= 504 - 240
= 264 km
Time that Oscar needed to reach his destination after the two met
= 264 ÷ 80
= 3
2480 = 3
310 h
Answer(s): (a) 88 km/h; (b) 3
310 h