City U and City V are 414 km apart. At 6.12 p.m., Carl is travelling at a uniform speed left City U for City V while Vincent set off from City V to City U along the same road at a uniform speed, which was 9 km/h slower than that of Carl. The two met at 8.12 p.m.
- Find the speed of Carl.
- If Vincent 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 Carl and Vincent to travel from 6.12 p.m. to 8.12 p.m. = 2 h
Average speed of Carl and Vincent
= 414 ÷ 2
= 207 km/h
Carl's speed
= (207 + 9) ÷ 2
= 216 ÷ 2
= 108 km/h
(b)
Vincent's speed
= 108 - 9
= 99 km/h
Distance that Vincent travelled in 2 h
= 2 x 99
= 198 km
Remaining distance that Vincent needed to travel
= 414 - 198
= 216 km
Time that Vincent needed to reach his destination after the two met
= 216 ÷ 99
= 2
1899 = 2
211 h
Answer(s): (a) 108 km/h; (b) 2
211 h