City L and City M is 504 km apart. Pierre left City L for City M at 11.00 a.m. travelling at an average speed of 72 km/h. Riordan left City L later than Pierre and caught up with him at 1.00 p.m. Riordan was travelling at a speed of 108 km/h.

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

(a)
From 11.00 a.m. to 1.00 p.m. = 2 h

Distance that Pierre covered when Riordan caught up with Pierre
= 2 x 72
= 144 km

Time that Riordan took to travel 144 km
= 144 ÷ 108
= 1¹₃ h

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

Time that Riordan left City L:
1 h 20 min before 1.00 p.m. = 11.40 a.m.

(b)
Remaining distance that they had to cover to reach City M
= 504 - 144
= 360 km

Duration that Riordan had to travel before reaching City M
= 360 ÷ 108
= 3¹₃ h

Duration that Pierre had to travel before reaching City M
= 360 ÷ 72
= 5 h

Duration that Pierre took to arrive later than Riordan in City M
= 5 - 3¹₃
= 1²₃ h

Answer(s): (a) 11.40 a.m.; (b) 1²₃ h