City S and City T is 462 km apart. Mark left City S for City T at 11.00 a.m. travelling at an average speed of 77 km/h. Billy left City S later than Mark and caught up with him at 1.00 p.m. Billy was travelling at a speed of 84 km/h.

1. At what time did Billy leave City S?
2. How much later did Mark arrive in City T than Billy? 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 Mark covered when Billy caught up with Mark
= 2 x 77
= 154 km

Time that Billy took to travel 154 km
= 154 ÷ 84
= 1⁵₆ h

1 h = 60 min
⁵₆ h = ⁵₆ x 60 = 50 min
1⁵₆ h = 1 h 50 min

Time that Billy left City S:
1 h 50 min before 1.00 p.m. = 11.10 a.m.

(b)
Remaining distance that they had to cover to reach City T
= 462 - 154
= 308 km

Duration that Billy had to travel before reaching City T
= 308 ÷ 84
= 3²₃ h

Duration that Mark had to travel before reaching City T
= 308 ÷ 77
= 4 h

Duration that Mark took to arrive later than Billy in City T
= 4 - 3²₃
= ¹₃ h

Answer(s): (a) 11.10 a.m.; (b) ¹₃ h