City L and City M is 441 km apart. Ethan left City L for City M at 11.00 a.m. travelling at an average speed of 63 km/h. Simon left City L later than Ethan and caught up with him at 2.00 p.m. Simon was travelling at a speed of 81 km/h.

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

(a)
From 11.00 a.m. to 2.00 p.m. = 3 h

Distance that Ethan covered when Simon caught up with Ethan
= 3 x 63
= 189 km

Time that Simon took to travel 189 km
= 189 ÷ 81
= 2¹₃ h

1 h = 60 min
¹₃ h = ¹₃ x 60 = 20 min
2¹₃ h = 2 h 20 min

Time that Simon left City L:
2 h 20 min before 2.00 p.m. = 11.40 a.m.

(b)
Remaining distance that they had to cover to reach City M
= 441 - 189
= 252 km

Duration that Simon had to travel before reaching City M
= 252 ÷ 81
= 3¹₉ h

Duration that Ethan had to travel before reaching City M
= 252 ÷ 63
= 4 h

Duration that Ethan took to arrive later than Simon in City M
= 4 - 3¹₉
= ⁸₉ h

Answer(s): (a) 11.40 a.m.; (b) ⁸₉ h