City N and City P are 400 km apart. At 3.44 p.m., Michael is travelling at a uniform speed left City N for City P while Ian 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 5.44 p.m.
- Find the speed of Michael.
- 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 Michael and Ian to travel from 3.44 p.m. to 5.44 p.m. = 2 h
Average speed of Michael and Ian
= 400 ÷ 2
= 200 km/h
Michael's speed
= (200 + 10) ÷ 2
= 210 ÷ 2
= 105 km/h
(b)
Ian's speed
= 105 - 10
= 95 km/h
Distance that Ian travelled in 2 h
= 2 x 95
= 190 km
Remaining distance that Ian needed to travel
= 400 - 190
= 210 km
Time that Ian needed to reach his destination after the two met
= 210 ÷ 95
= 2
2095 = 2
419 h
Answer(s): (a) 105 km/h; (b) 2
419 h