City E and City F is 546 km apart. Brandon left City E for City F at 10.00 a.m. travelling at an average speed of 78 km/h. Ethan left City E later than Brandon and caught up with him at 1.00 p.m. Ethan was travelling at a speed of 108 km/h.
- At what time did Ethan leave City E?
- How much later did Brandon arrive in City F than Ethan? Express your answer in h as a fraction or mixed number.
(a)
From 10.00 a.m. to 1.00 p.m. = 3 h
Distance that Brandon covered when Ethan caught up with Brandon
= 3 x 78
= 234 km
Time that Ethan 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 Ethan left City E:
2 h 10 min before 1.00 p.m. = 10.50 a.m.
(b)
Remaining distance that they had to cover to reach City F
= 546 - 234
= 312 km
Duration that Ethan had to travel before reaching City F
= 312 ÷ 108
= 2
89 h
Duration that Brandon had to travel before reaching City F
= 312 ÷ 78
= 4 h
Duration that Brandon took to arrive later than Ethan in City F
= 4 - 2
89= 1
19 h
Answer(s): (a) 10.50 a.m.; (b) 1
19 h
