City K and City L are 356 km apart. At 1.21 p.m., Paul is travelling at a uniform speed left City K for City L while Reggie set off from City L to City K along the same road at a uniform speed, which was 10 km/h slower than that of Paul. The two met at 3.21 p.m.
- Find the speed of Paul.
- If Reggie 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 Reggie to travel from 1.21 p.m. to 3.21 p.m. = 2 h
Average speed of Paul and Reggie
= 356 ÷ 2
= 178 km/h
Paul's speed
= (178 + 10) ÷ 2
= 188 ÷ 2
= 94 km/h
(b)
Reggie's speed
= 94 - 10
= 84 km/h
Distance that Reggie travelled in 2 h
= 2 x 84
= 168 km
Remaining distance that Reggie needed to travel
= 356 - 168
= 188 km
Time that Reggie needed to reach his destination after the two met
= 188 ÷ 84
= 2
2084 = 2
521 h
Answer(s): (a) 94 km/h; (b) 2
521 h