City T and City U are 330 km apart. At 6.12 p.m., Howard is travelling at a uniform speed left City T for City U while Sam set off from City U to City T along the same road at a uniform speed, which was 9 km/h slower than that of Howard. The two met at 8.12 p.m.
- Find the speed of Howard.
- If Sam 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 Howard and Sam to travel from 6.12 p.m. to 8.12 p.m. = 2 h
Average speed of Howard and Sam
= 330 ÷ 2
= 165 km/h
Howard's speed
= (165 + 9) ÷ 2
= 174 ÷ 2
= 87 km/h
(b)
Sam's speed
= 87 - 9
= 78 km/h
Distance that Sam travelled in 2 h
= 2 x 78
= 156 km
Remaining distance that Sam needed to travel
= 330 - 156
= 174 km
Time that Sam needed to reach his destination after the two met
= 174 ÷ 78
= 2
1878 = 2
313 h
Answer(s): (a) 87 km/h; (b) 2
313 h