City T and City U are 580 km apart. At 2.44 p.m., Daniel is travelling at a uniform speed left City T for City U while Howard set off from City U to City T along the same road at a uniform speed, which was 12 km/h slower than that of Daniel. The two met at 7.44 p.m.
- Find the speed of Daniel.
- If Howard 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 Daniel and Howard to travel from 2.44 p.m. to 7.44 p.m. = 5 h
Average speed of Daniel and Howard
= 580 ÷ 5
= 116 km/h
Daniel's speed
= (116 + 12) ÷ 2
= 128 ÷ 2
= 64 km/h
(b)
Howard's speed
= 64 - 12
= 52 km/h
Distance that Howard travelled in 5 h
= 5 x 52
= 260 km
Remaining distance that Howard needed to travel
= 580 - 260
= 320 km
Time that Howard needed to reach his destination after the two met
= 320 ÷ 52
= 6
852 = 6
213 h
Answer(s): (a) 64 km/h; (b) 6
213 h