City M and City N is 420 km apart. Billy left City M for City N at 7.00 a.m. travelling at an average speed of 70 km/h. Archie left City M later than Billy and caught up with him at 11.00 a.m. Archie was travelling at a speed of 105 km/h.

1. At what time did Archie leave City M?
2. How much later did Billy arrive in City N than Archie? 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 Billy covered when Archie caught up with Billy
= 4 x 70
= 280 km

Time that Archie took to travel 280 km
= 280 ÷ 105
= 2²₃ h

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

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

(b)
Remaining distance that they had to cover to reach City N
= 420 - 280
= 140 km

Duration that Archie had to travel before reaching City N
= 140 ÷ 105
= 1¹₃ h

Duration that Billy had to travel before reaching City N
= 140 ÷ 70
= 2 h

Duration that Billy took to arrive later than Archie in City N
= 2 - 1¹₃
= ²₃ h

Answer(s): (a) 8.20 a.m.; (b) ²₃ h