City Y and City Z is 483 km apart. Jeremy left City Y for City Z at 11.00 a.m. travelling at an average speed of 69 km/h. Liam left City Y later than Jeremy and caught up with him at 2.00 p.m. Liam was travelling at a speed of 108 km/h.

1. At what time did Liam leave City Y?
2. How much later did Jeremy arrive in City Z than Liam? 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 Jeremy covered when Liam caught up with Jeremy
= 3 x 69
= 207 km

Time that Liam 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 Liam left City Y:
1 h 55 min before 2.00 p.m. = 12.05 p.m.

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

Duration that Liam had to travel before reaching City Z
= 276 ÷ 108
= 2⁵₉ h

Duration that Jeremy had to travel before reaching City Z
= 276 ÷ 69
= 4 h

Duration that Jeremy took to arrive later than Liam in City Z
= 4 - 2⁵₉
= 1⁴₉ h

Answer(s): (a) 12.05 p.m.; (b) 1⁴₉ h