City M and City N are 459 km apart. At 1.29 p.m., Michael is travelling at a uniform speed left City M for City N while Asher set off from City N to City M along the same road at a uniform speed, which was 9 km/h slower than that of Michael. The two met at 4.29 p.m.
- Find the speed of Michael.
- If Asher 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 Asher to travel from 1.29 p.m. to 4.29 p.m. = 3 h
Average speed of Michael and Asher
= 459 ÷ 3
= 153 km/h
Michael's speed
= (153 + 9) ÷ 2
= 162 ÷ 2
= 81 km/h
(b)
Asher's speed
= 81 - 9
= 72 km/h
Distance that Asher travelled in 3 h
= 3 x 72
= 216 km
Remaining distance that Asher needed to travel
= 459 - 216
= 243 km
Time that Asher needed to reach his destination after the two met
= 243 ÷ 72
= 3
2772 = 3
38 h
Answer(s): (a) 81 km/h; (b) 3
38 h