City B and City C are 320 km apart. At 3.51 p.m., Michael is travelling at a uniform speed left City B for City C while Japheth set off from City C to City B along the same road at a uniform speed, which was 10 km/h slower than that of Michael. The two met at 5.51 p.m.
- Find the speed of Michael.
- If Japheth 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 Japheth to travel from 3.51 p.m. to 5.51 p.m. = 2 h
Average speed of Michael and Japheth
= 320 ÷ 2
= 160 km/h
Michael's speed
= (160 + 10) ÷ 2
= 170 ÷ 2
= 85 km/h
(b)
Japheth's speed
= 85 - 10
= 75 km/h
Distance that Japheth travelled in 2 h
= 2 x 75
= 150 km
Remaining distance that Japheth needed to travel
= 320 - 150
= 170 km
Time that Japheth needed to reach his destination after the two met
= 170 ÷ 75
= 2
2075 = 2
415 h
Answer(s): (a) 85 km/h; (b) 2
415 h