City S and City T are 396 km apart. At 5.41 p.m., Gabriel is travelling at a uniform speed left City S for City T while Charlie set off from City T to City S along the same road at a uniform speed, which was 6 km/h slower than that of Gabriel. The two met at 8.41 p.m.
- Find the speed of Gabriel.
- If Charlie 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 Gabriel and Charlie to travel from 5.41 p.m. to 8.41 p.m. = 3 h
Average speed of Gabriel and Charlie
= 396 ÷ 3
= 132 km/h
Gabriel's speed
= (132 + 6) ÷ 2
= 138 ÷ 2
= 69 km/h
(b)
Charlie's speed
= 69 - 6
= 63 km/h
Distance that Charlie travelled in 3 h
= 3 x 63
= 189 km
Remaining distance that Charlie needed to travel
= 396 - 189
= 207 km
Time that Charlie needed to reach his destination after the two met
= 207 ÷ 63
= 3
1863 = 3
27 h
Answer(s): (a) 69 km/h; (b) 3
27 h