City N and City P are 560 km apart. At 6.12 p.m., Andy is travelling at a uniform speed left City N for City P while Ethan set off from City P to City N along the same road at a uniform speed, which was 12 km/h slower than that of Andy. The two met at 10.12 p.m.
- Find the speed of Andy.
- If Ethan 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 Andy and Ethan to travel from 6.12 p.m. to 10.12 p.m. = 4 h
Average speed of Andy and Ethan
= 560 ÷ 4
= 140 km/h
Andy's speed
= (140 + 12) ÷ 2
= 152 ÷ 2
= 76 km/h
(b)
Ethan's speed
= 76 - 12
= 64 km/h
Distance that Ethan travelled in 4 h
= 4 x 64
= 256 km
Remaining distance that Ethan needed to travel
= 560 - 256
= 304 km
Time that Ethan needed to reach his destination after the two met
= 304 ÷ 64
= 4
4864 = 4
34 h
Answer(s): (a) 76 km/h; (b) 4
34 h