City N and City P is 240 km apart. Jeremy left City N for City P at 11.00 a.m. travelling at an average speed of 60 km/h. Valen left City N later than Jeremy and caught up with him at 1.00 p.m. Valen was travelling at a speed of 96 km/h.

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

(a)
From 11.00 a.m. to 1.00 p.m. = 2 h

Distance that Jeremy covered when Valen caught up with Jeremy
= 2 x 60
= 120 km

Time that Valen took to travel 120 km
= 120 ÷ 96
= 1¹₄ h

1 h = 60 min
¹₄ h = ¹₄ x 60 = 15 min
1¹₄ h = 1 h 15 min

Time that Valen left City N:
1 h 15 min before 1.00 p.m. = 11.45 a.m.

(b)
Remaining distance that they had to cover to reach City P
= 240 - 120
= 120 km

Duration that Valen had to travel before reaching City P
= 120 ÷ 96
= 1¹₄ h

Duration that Jeremy had to travel before reaching City P
= 120 ÷ 60
= 2 h

Duration that Jeremy took to arrive later than Valen in City P
= 2 - 1¹₄
= ³₄ h

Answer(s): (a) 11.45 a.m.; (b) ³₄ h