City U and City V are 576 km apart. At 6.52 p.m., Daniel is travelling at a uniform speed left City U for City V while Ian set off from City V to City U along the same road at a uniform speed, which was 12 km/h slower than that of Daniel. The two met at 10.52 p.m.
- Find the speed of Daniel.
- If Ian 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 Ian to travel from 6.52 p.m. to 10.52 p.m. = 4 h
Average speed of Daniel and Ian
= 576 ÷ 4
= 144 km/h
Daniel's speed
= (144 + 12) ÷ 2
= 156 ÷ 2
= 78 km/h
(b)
Ian's speed
= 78 - 12
= 66 km/h
Distance that Ian travelled in 4 h
= 4 x 66
= 264 km
Remaining distance that Ian needed to travel
= 576 - 264
= 312 km
Time that Ian needed to reach his destination after the two met
= 312 ÷ 66
= 4
4866 = 4
811 h
Answer(s): (a) 78 km/h; (b) 4
811 h