City C and City D is 378 km apart. Peter left City C for City D at 9.00 a.m. travelling at an average speed of 63 km/h. Simon left City C later than Peter and caught up with him at 12.00 p.m. Simon was travelling at a speed of 81 km/h.

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

(a)
From 9.00 a.m. to 12.00 p.m. = 3 h

Distance that Peter covered when Simon caught up with Peter
= 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 C:
2 h 20 min before 12.00 p.m. = 9.40 a.m.

(b)
Remaining distance that they had to cover to reach City D
= 378 - 189
= 189 km

Duration that Simon had to travel before reaching City D
= 189 ÷ 81
= 2¹₃ h

Duration that Peter had to travel before reaching City D
= 189 ÷ 63
= 3 h

Duration that Peter took to arrive later than Simon in City D
= 3 - 2¹₃
= ²₃ h

Answer(s): (a) 9.40 a.m.; (b) ²₃ h