City X and City Y are 372 km apart. At 2.50 p.m., Valen is travelling at a uniform speed left City X for City Y while Luis 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 Valen. The two met at 5.50 p.m.
- Find the speed of Valen.
- If Luis 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 Luis to travel from 2.50 p.m. to 5.50 p.m. = 3 h
Average speed of Valen and Luis
= 372 ÷ 3
= 124 km/h
Valen's speed
= (124 + 10) ÷ 2
= 134 ÷ 2
= 67 km/h
(b)
Luis's speed
= 67 - 10
= 57 km/h
Distance that Luis travelled in 3 h
= 3 x 57
= 171 km
Remaining distance that Luis needed to travel
= 372 - 171
= 201 km
Time that Luis needed to reach his destination after the two met
= 201 ÷ 57
= 3
3057 = 3
1019 h
Answer(s): (a) 67 km/h; (b) 3
1019 h