City M and City N is 504 km apart. Zeph left City M for City N at 11.00 a.m. travelling at an average speed of 72 km/h. Archie left City M later than Zeph and caught up with him at 3.00 p.m. Archie was travelling at a speed of 108 km/h.

1. At what time did Archie leave City M?
2. How much later did Zeph arrive in City N than Archie? 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 Zeph covered when Archie caught up with Zeph
= 4 x 72
= 288 km

Time that Archie took to travel 288 km
= 288 ÷ 108
= 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 3.00 p.m. = 12.20 p.m.

(b)
Remaining distance that they had to cover to reach City N
= 504 - 288
= 216 km

Duration that Archie had to travel before reaching City N
= 216 ÷ 108
= 2 h

Duration that Zeph had to travel before reaching City N
= 216 ÷ 72
= 3 h

Duration that Zeph took to arrive later than Archie in City N
= 3 - 2
= 1 h

Answer(s): (a) 12.20 p.m.; (b) 1 h