City J and City K are 435 km apart. At 1.48 p.m., Asher is travelling at a uniform speed left City J for City K while Pierre set off from City K to City J along the same road at a uniform speed, which was 5 km/h slower than that of Asher. The two met at 4.48 p.m.
- Find the speed of Asher.
- If Pierre 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 Asher and Pierre to travel from 1.48 p.m. to 4.48 p.m. = 3 h
Average speed of Asher and Pierre
= 435 ÷ 3
= 145 km/h
Asher's speed
= (145 + 5) ÷ 2
= 150 ÷ 2
= 75 km/h
(b)
Pierre's speed
= 75 - 5
= 70 km/h
Distance that Pierre travelled in 3 h
= 3 x 70
= 210 km
Remaining distance that Pierre needed to travel
= 435 - 210
= 225 km
Time that Pierre needed to reach his destination after the two met
= 225 ÷ 70
= 3
1570 = 3
314 h
Answer(s): (a) 75 km/h; (b) 3
314 h