City L and City M is 468 km apart. Peter left City L for City M at 9.00 a.m. travelling at an average speed of 78 km/h. Bryan left City L later than Peter and caught up with him at 11.00 a.m. Bryan was travelling at a speed of 117 km/h.

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

(a)
From 9.00 a.m. to 11.00 a.m. = 2 h

Distance that Peter covered when Bryan caught up with Peter
= 2 x 78
= 156 km

Time that Bryan took to travel 156 km
= 156 ÷ 117
= 1¹₃ h

1 h = 60 min
¹₃ h = ¹₃ x 60 = 20 min
1¹₃ h = 1 h 20 min

Time that Bryan left City L:
1 h 20 min before 11.00 a.m. = 9.40 a.m.

(b)
Remaining distance that they had to cover to reach City M
= 468 - 156
= 312 km

Duration that Bryan had to travel before reaching City M
= 312 ÷ 117
= 2²₃ h

Duration that Peter had to travel before reaching City M
= 312 ÷ 78
= 4 h

Duration that Peter took to arrive later than Bryan in City M
= 4 - 2²₃
= 1¹₃ h

Answer(s): (a) 9.40 a.m.; (b) 1¹₃ h