City P and City Q are 378 km apart. At 5.28 p.m., Paul is travelling at a uniform speed left City P for City Q while Ryan 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 Paul. The two met at 8.28 p.m.
- Find the speed of Paul.
- If Ryan 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 Paul and Ryan to travel from 5.28 p.m. to 8.28 p.m. = 3 h
Average speed of Paul and Ryan
= 378 ÷ 3
= 126 km/h
Paul's speed
= (126 + 12) ÷ 2
= 138 ÷ 2
= 69 km/h
(b)
Ryan's speed
= 69 - 12
= 57 km/h
Distance that Ryan travelled in 3 h
= 3 x 57
= 171 km
Remaining distance that Ryan needed to travel
= 378 - 171
= 207 km
Time that Ryan needed to reach his destination after the two met
= 207 ÷ 57
= 3
3657 = 3
1219 h
Answer(s): (a) 69 km/h; (b) 3
1219 h