City X and City Y is 456 km apart. Elijah left City X for City Y at 10.00 a.m. travelling at an average speed of 76 km/h. Riordan left City X later than Elijah and caught up with him at 12.00 p.m. Riordan was travelling at a speed of 114 km/h.
- At what time did Riordan leave City X?
- How much later did Elijah arrive in City Y than Riordan? Express your answer in h as a fraction or mixed number.
(a)
From 10.00 a.m. to 12.00 p.m. = 2 h
Distance that Elijah covered when Riordan caught up with Elijah
= 2 x 76
= 152 km
Time that Riordan took to travel 152 km
= 152 ÷ 114
= 1
13 h
1 h = 60 min
13 h =
13 x 60 = 20 min
1
13 h = 1 h 20 min
Time that Riordan left City X:
1 h 20 min before 12.00 p.m. = 10.40 a.m.
(b)
Remaining distance that they had to cover to reach City Y
= 456 - 152
= 304 km
Duration that Riordan had to travel before reaching City Y
= 304 ÷ 114
= 2
23 h
Duration that Elijah had to travel before reaching City Y
= 304 ÷ 76
= 4 h
Duration that Elijah took to arrive later than Riordan in City Y
= 4 - 2
23= 1
13 h
Answer(s): (a) 10.40 a.m.; (b) 1
13 h