City F and City G are 360 km apart. At 6.34 p.m., Paul is travelling at a uniform speed left City F for City G while Bryan set off from City G to City F along the same road at a uniform speed, which was 12 km/h slower than that of Paul. The two met at 9.34 p.m.
- Find the speed of Paul.
- If Bryan 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 Bryan to travel from 6.34 p.m. to 9.34 p.m. = 3 h
Average speed of Paul and Bryan
= 360 ÷ 3
= 120 km/h
Paul's speed
= (120 + 12) ÷ 2
= 132 ÷ 2
= 66 km/h
(b)
Bryan's speed
= 66 - 12
= 54 km/h
Distance that Bryan travelled in 3 h
= 3 x 54
= 162 km
Remaining distance that Bryan needed to travel
= 360 - 162
= 198 km
Time that Bryan needed to reach his destination after the two met
= 198 ÷ 54
= 3
3654 = 3
23 h
Answer(s): (a) 66 km/h; (b) 3
23 h