City M and City N is 693 km apart. David left City M for City N at 11.00 a.m. travelling at an average speed of 77 km/h. Bryan left City M later than David and caught up with him at 3.00 p.m. Bryan was travelling at a speed of 112 km/h.

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

(a)
From 11.00 a.m. to 3.00 p.m. = 4 h

Distance that David covered when Bryan caught up with David
= 4 x 77
= 308 km

Time that Bryan took to travel 308 km
= 308 ÷ 112
= 2³₄ h

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

Time that Bryan left City M:
2 h 45 min before 3.00 p.m. = 12.15 p.m.

(b)
Remaining distance that they had to cover to reach City N
= 693 - 308
= 385 km

Duration that Bryan had to travel before reaching City N
= 385 ÷ 112
= 3⁷₁₆ h

Duration that David had to travel before reaching City N
= 385 ÷ 77
= 5 h

Duration that David took to arrive later than Bryan in City N
= 5 - 3⁷₁₆
= 1⁹₁₆ h

Answer(s): (a) 12.15 p.m.; (b) 1⁹₁₆ h