City U and City V are 316 km apart. At 4.47 p.m., Paul is travelling at a uniform speed left City U for City V while Rael set off from City V to City U along the same road at a uniform speed, which was 6 km/h slower than that of Paul. The two met at 6.47 p.m.
- Find the speed of Paul.
- If Rael 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 Rael to travel from 4.47 p.m. to 6.47 p.m. = 2 h
Average speed of Paul and Rael
= 316 ÷ 2
= 158 km/h
Paul's speed
= (158 + 6) ÷ 2
= 164 ÷ 2
= 82 km/h
(b)
Rael's speed
= 82 - 6
= 76 km/h
Distance that Rael travelled in 2 h
= 2 x 76
= 152 km
Remaining distance that Rael needed to travel
= 316 - 152
= 164 km
Time that Rael needed to reach his destination after the two met
= 164 ÷ 76
= 2
1276 = 2
319 h
Answer(s): (a) 82 km/h; (b) 2
319 h