City N and City P are 552 km apart. At 5.12 p.m., Michael is travelling at a uniform speed left City N for City P while David set off from City P to City N along the same road at a uniform speed, which was 10 km/h slower than that of Michael. The two met at 9.12 p.m.
- Find the speed of Michael.
- If David 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 Michael and David to travel from 5.12 p.m. to 9.12 p.m. = 4 h
Average speed of Michael and David
= 552 ÷ 4
= 138 km/h
Michael's speed
= (138 + 10) ÷ 2
= 148 ÷ 2
= 74 km/h
(b)
David's speed
= 74 - 10
= 64 km/h
Distance that David travelled in 4 h
= 4 x 64
= 256 km
Remaining distance that David needed to travel
= 552 - 256
= 296 km
Time that David needed to reach his destination after the two met
= 296 ÷ 64
= 4
4064 = 4
58 h
Answer(s): (a) 74 km/h; (b) 4
58 h