City P and City Q is 520 km apart. Jenson left City P for City Q at 9.00 a.m. travelling at an average speed of 65 km/h. Rael left City P later than Jenson and caught up with him at 12.00 p.m. Rael was travelling at a speed of 90 km/h.

1. At what time did Rael leave City P?
2. How much later did Jenson arrive in City Q than Rael? 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 Jenson covered when Rael caught up with Jenson
= 3 x 65
= 195 km

Time that Rael took to travel 195 km
= 195 ÷ 90
= 2¹₆ h

1 h = 60 min
¹₆ h = ¹₆ x 60 = 10 min
2¹₆ h = 2 h 10 min

Time that Rael left City P:
2 h 10 min before 12.00 p.m. = 9.50 a.m.

(b)
Remaining distance that they had to cover to reach City Q
= 520 - 195
= 325 km

Duration that Rael had to travel before reaching City Q
= 325 ÷ 90
= 3¹¹₁₈ h

Duration that Jenson had to travel before reaching City Q
= 325 ÷ 65
= 5 h

Duration that Jenson took to arrive later than Rael in City Q
= 5 - 3¹¹₁₈
= 1⁷₁₈ h

Answer(s): (a) 9.50 a.m.; (b) 1⁷₁₈ h