City V and City W are 432 km apart. At 1.30 p.m., Tim is travelling at a uniform speed left City V for City W while Luis set off from City W to City V along the same road at a uniform speed, which was 12 km/h slower than that of Tim. The two met at 3.30 p.m.
- Find the speed of Tim.
- 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 Tim and Luis to travel from 1.30 p.m. to 3.30 p.m. = 2 h
Average speed of Tim and Luis
= 432 ÷ 2
= 216 km/h
Tim's speed
= (216 + 12) ÷ 2
= 228 ÷ 2
= 114 km/h
(b)
Luis's speed
= 114 - 12
= 102 km/h
Distance that Luis travelled in 2 h
= 2 x 102
= 204 km
Remaining distance that Luis needed to travel
= 432 - 204
= 228 km
Time that Luis needed to reach his destination after the two met
= 228 ÷ 102
= 2
24102 = 2
417 h
Answer(s): (a) 114 km/h; (b) 2
417 h