City Y and City Z is 372 km apart. Jeremy left City Y for City Z at 9.00 a.m. travelling at an average speed of 62 km/h. Peter left City Y later than Jeremy and caught up with him at 1.00 p.m. Peter was travelling at a speed of 93 km/h.

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

(a)
From 9.00 a.m. to 1.00 p.m. = 4 h

Distance that Jeremy covered when Peter caught up with Jeremy
= 4 x 62
= 248 km

Time that Peter took to travel 248 km
= 248 ÷ 93
= 2²₃ h

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

Time that Peter left City Y:
2 h 40 min before 1.00 p.m. = 10.20 a.m.

(b)
Remaining distance that they had to cover to reach City Z
= 372 - 248
= 124 km

Duration that Peter had to travel before reaching City Z
= 124 ÷ 93
= 1¹₃ h

Duration that Jeremy had to travel before reaching City Z
= 124 ÷ 62
= 2 h

Duration that Jeremy took to arrive later than Peter in City Z
= 2 - 1¹₃
= ²₃ h

Answer(s): (a) 10.20 a.m.; (b) ²₃ h