City M and City N are 408 km apart. At 1.13 p.m., David is travelling at a uniform speed left City M for City N while Reggie set off from City N to City M along the same road at a uniform speed, which was 8 km/h slower than that of David. The two met at 4.13 p.m.
- Find the speed of David.
- 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 David and Reggie to travel from 1.13 p.m. to 4.13 p.m. = 3 h
Average speed of David and Reggie
= 408 ÷ 3
= 136 km/h
David's speed
= (136 + 8) ÷ 2
= 144 ÷ 2
= 72 km/h
(b)
Reggie's speed
= 72 - 8
= 64 km/h
Distance that Reggie travelled in 3 h
= 3 x 64
= 192 km
Remaining distance that Reggie needed to travel
= 408 - 192
= 216 km
Time that Reggie needed to reach his destination after the two met
= 216 ÷ 64
= 3
2464 = 3
38 h
Answer(s): (a) 72 km/h; (b) 3
38 h