City P and City Q is 666 km apart. Perry left City P for City Q at 7.00 a.m. travelling at an average speed of 74 km/h. Brandon left City P later than Perry and caught up with him at 11.00 a.m. Brandon was travelling at a speed of 111 km/h.

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

(a)
From 7.00 a.m. to 11.00 a.m. = 4 h

Distance that Perry covered when Brandon caught up with Perry
= 4 x 74
= 296 km

Time that Brandon took to travel 296 km
= 296 ÷ 111
= 2²₃ h

1 h = 60 min
²₃ h = ²₃ x 60 = 40 min
2²₃ h = 2 h 40 min

Time that Brandon left City P:
2 h 40 min before 11.00 a.m. = 8.20 a.m.

(b)
Remaining distance that they had to cover to reach City Q
= 666 - 296
= 370 km

Duration that Brandon had to travel before reaching City Q
= 370 ÷ 111
= 3¹₃ h

Duration that Perry had to travel before reaching City Q
= 370 ÷ 74
= 5 h

Duration that Perry took to arrive later than Brandon in City Q
= 5 - 3¹₃
= 1²₃ h

Answer(s): (a) 8.20 a.m.; (b) 1²₃ h