City B and City C are 342 km apart. At 6.17 p.m., Valen is travelling at a uniform speed left City B for City C while Billy set off from City C to City B along the same road at a uniform speed, which was 9 km/h slower than that of Valen. The two met at 8.17 p.m.
- Find the speed of Valen.
- If Billy 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 Valen and Billy to travel from 6.17 p.m. to 8.17 p.m. = 2 h
Average speed of Valen and Billy
= 342 ÷ 2
= 171 km/h
Valen's speed
= (171 + 9) ÷ 2
= 180 ÷ 2
= 90 km/h
(b)
Billy's speed
= 90 - 9
= 81 km/h
Distance that Billy travelled in 2 h
= 2 x 81
= 162 km
Remaining distance that Billy needed to travel
= 342 - 162
= 180 km
Time that Billy needed to reach his destination after the two met
= 180 ÷ 81
= 2
1881 = 2
29 h
Answer(s): (a) 90 km/h; (b) 2
29 h