City V and City W is 539 km apart. Perry left City V for City W at 11.00 a.m. travelling at an average speed of 77 km/h. Fred left City V later than Perry and caught up with him at 2.00 p.m. Fred was travelling at a speed of 84 km/h.

1. At what time did Fred leave City V?
2. How much later did Perry arrive in City W than Fred? Express your answer in h as a fraction or mixed number.

(a)
From 11.00 a.m. to 2.00 p.m. = 3 h

Distance that Perry covered when Fred caught up with Perry
= 3 x 77
= 231 km

Time that Fred took to travel 231 km
= 231 ÷ 84
= 2³₄ h

1 h = 60 min
³₄ h = ³₄ x 60 = 45 min
2³₄ h = 2 h 45 min

Time that Fred left City V:
2 h 45 min before 2.00 p.m. = 11.15 a.m.

(b)
Remaining distance that they had to cover to reach City W
= 539 - 231
= 308 km

Duration that Fred had to travel before reaching City W
= 308 ÷ 84
= 3²₃ h

Duration that Perry had to travel before reaching City W
= 308 ÷ 77
= 4 h

Duration that Perry took to arrive later than Fred in City W
= 4 - 3²₃
= ¹₃ h

Answer(s): (a) 11.15 a.m.; (b) ¹₃ h