City P and City Q is 483 km apart. Valen left City P for City Q at 7.00 a.m. travelling at an average speed of 69 km/h. Carl left City P later than Valen and caught up with him at 10.00 a.m. Carl was travelling at a speed of 108 km/h.

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

(a)
From 7.00 a.m. to 10.00 a.m. = 3 h

Distance that Valen covered when Carl caught up with Valen
= 3 x 69
= 207 km

Time that Carl took to travel 207 km
= 207 ÷ 108
= 1¹¹₁₂ h

1 h = 60 min
¹¹₁₂ h = ¹¹₁₂ x 60 = 55 min
1¹¹₁₂ h = 1 h 55 min

Time that Carl left City P:
1 h 55 min before 10.00 a.m. = 8.05 a.m.

(b)
Remaining distance that they had to cover to reach City Q
= 483 - 207
= 276 km

Duration that Carl had to travel before reaching City Q
= 276 ÷ 108
= 2⁵₉ h

Duration that Valen had to travel before reaching City Q
= 276 ÷ 69
= 4 h

Duration that Valen took to arrive later than Carl in City Q
= 4 - 2⁵₉
= 1⁴₉ h

Answer(s): (a) 8.05 a.m.; (b) 1⁴₉ h