City N and City P are 372 km apart. At 1.25 p.m., Japheth is travelling at a uniform speed left City N for City P while Paul set off from City P to City N along the same road at a uniform speed, which was 12 km/h slower than that of Japheth. The two met at 4.25 p.m.
- Find the speed of Japheth.
- If Paul 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 Japheth and Paul to travel from 1.25 p.m. to 4.25 p.m. = 3 h
Average speed of Japheth and Paul
= 372 ÷ 3
= 124 km/h
Japheth's speed
= (124 + 12) ÷ 2
= 136 ÷ 2
= 68 km/h
(b)
Paul's speed
= 68 - 12
= 56 km/h
Distance that Paul travelled in 3 h
= 3 x 56
= 168 km
Remaining distance that Paul needed to travel
= 372 - 168
= 204 km
Time that Paul needed to reach his destination after the two met
= 204 ÷ 56
= 3
3656 = 3
914 h
Answer(s): (a) 68 km/h; (b) 3
914 h