City M and City N is 552 km apart. Lee left City M for City N at 11.00 a.m. travelling at an average speed of 69 km/h. Peter left City M later than Lee and caught up with him at 2.00 p.m. Peter was travelling at a speed of 92 km/h.

1. At what time did Peter leave City M?
2. How much later did Lee arrive in City N than Peter? 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 Lee covered when Peter caught up with Lee
= 3 x 69
= 207 km

Time that Peter took to travel 207 km
= 207 ÷ 92
= 2¹₄ h

1 h = 60 min
¹₄ h = ¹₄ x 60 = 15 min
2¹₄ h = 2 h 15 min

Time that Peter left City M:
2 h 15 min before 2.00 p.m. = 11.45 a.m.

(b)
Remaining distance that they had to cover to reach City N
= 552 - 207
= 345 km

Duration that Peter had to travel before reaching City N
= 345 ÷ 92
= 3³₄ h

Duration that Lee had to travel before reaching City N
= 345 ÷ 69
= 5 h

Duration that Lee took to arrive later than Peter in City N
= 5 - 3³₄
= 1¹₄ h

Answer(s): (a) 11.45 a.m.; (b) 1¹₄ h