City S and City T is 462 km apart. Daniel left City S for City T at 10.00 a.m. travelling at an average speed of 77 km/h. Peter left City S later than Daniel and caught up with him at 1.00 p.m. Peter was travelling at a speed of 84 km/h.

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

(a)
From 10.00 a.m. to 1.00 p.m. = 3 h

Distance that Daniel covered when Peter caught up with Daniel
= 3 x 77
= 231 km

Time that Peter took to travel 231 km
= 231 ÷ 84
= 2³₄ h

1 h = 60 min
³₄ h = ³₄ x 60 = 45 min
2³₄ h = 2 h 45 min

Time that Peter left City S:
2 h 45 min before 1.00 p.m. = 10.15 a.m.

(b)
Remaining distance that they had to cover to reach City T
= 462 - 231
= 231 km

Duration that Peter had to travel before reaching City T
= 231 ÷ 84
= 2³₄ h

Duration that Daniel had to travel before reaching City T
= 231 ÷ 77
= 3 h

Duration that Daniel took to arrive later than Peter in City T
= 3 - 2³₄
= ¹₄ h

Answer(s): (a) 10.15 a.m.; (b) ¹₄ h