City J and City K is 624 km apart. Billy left City J for City K at 7.00 a.m. travelling at an average speed of 78 km/h. Jeremy left City J later than Billy and caught up with him at 10.00 a.m. Jeremy was travelling at a speed of 108 km/h.
- At what time did Jeremy leave City J?
- How much later did Billy arrive in City K than Jeremy? Express your answer in h as a fraction or mixed number.
(a)
From 7.00 a.m. to 10.00 a.m. = 3 h
Distance that Billy covered when Jeremy caught up with Billy
= 3 x 78
= 234 km
Time that Jeremy took to travel 234 km
= 234 ÷ 108
= 2
16 h
1 h = 60 min
16 h =
16 x 60 = 10 min
2
16 h = 2 h 10 min
Time that Jeremy left City J:
2 h 10 min before 10.00 a.m. = 7.50 a.m.
(b)
Remaining distance that they had to cover to reach City K
= 624 - 234
= 390 km
Duration that Jeremy had to travel before reaching City K
= 390 ÷ 108
= 3
1118 h
Duration that Billy had to travel before reaching City K
= 390 ÷ 78
= 5 h
Duration that Billy took to arrive later than Jeremy in City K
= 5 - 3
1118= 1
718 h
Answer(s): (a) 7.50 a.m.; (b) 1
718 h