City M and City N is 504 km apart. Bobby left City M for City N at 10.00 a.m. travelling at an average speed of 63 km/h. Ben left City M later than Bobby and caught up with him at 2.00 p.m. Ben was travelling at a speed of 108 km/h.

1. At what time did Ben leave City M?
2. How much later did Bobby arrive in City N than Ben? Express your answer in h as a fraction or mixed number.

(a)
From 10.00 a.m. to 2.00 p.m. = 4 h

Distance that Bobby covered when Ben caught up with Bobby
= 4 x 63
= 252 km

Time that Ben took to travel 252 km
= 252 ÷ 108
= 2¹₃ h

1 h = 60 min
¹₃ h = ¹₃ x 60 = 20 min
2¹₃ h = 2 h 20 min

Time that Ben left City M:
2 h 20 min before 2.00 p.m. = 11.40 a.m.

(b)
Remaining distance that they had to cover to reach City N
= 504 - 252
= 252 km

Duration that Ben had to travel before reaching City N
= 252 ÷ 108
= 2¹₃ h

Duration that Bobby had to travel before reaching City N
= 252 ÷ 63
= 4 h

Duration that Bobby took to arrive later than Ben in City N
= 4 - 2¹₃
= 1²₃ h

Answer(s): (a) 11.40 a.m.; (b) 1²₃ h