City P and City Q are 540 km apart. At 4.28 p.m., Tim is travelling at a uniform speed left City P for City Q while Japheth set off from City Q to City P along the same road at a uniform speed, which was 12 km/h slower than that of Tim. The two met at 7.28 p.m.
- Find the speed of Tim.
- If Japheth 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 Japheth to travel from 4.28 p.m. to 7.28 p.m. = 3 h
Average speed of Tim and Japheth
= 540 ÷ 3
= 180 km/h
Tim's speed
= (180 + 12) ÷ 2
= 192 ÷ 2
= 96 km/h
(b)
Japheth's speed
= 96 - 12
= 84 km/h
Distance that Japheth travelled in 3 h
= 3 x 84
= 252 km
Remaining distance that Japheth needed to travel
= 540 - 252
= 288 km
Time that Japheth needed to reach his destination after the two met
= 288 ÷ 84
= 3
3684 = 3
37 h
Answer(s): (a) 96 km/h; (b) 3
37 h