City G and City H is 490 km apart. Tom left City G for City H at 10.00 a.m. travelling at an average speed of 70 km/h. Luis left City G later than Tom and caught up with him at 1.00 p.m. Luis was travelling at a speed of 90 km/h.

1. At what time did Luis leave City G?
2. How much later did Tom arrive in City H than Luis? 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 Tom covered when Luis caught up with Tom
= 3 x 70
= 210 km

Time that Luis took to travel 210 km
= 210 ÷ 90
= 2¹₃ h

1 h = 60 min
¹₃ h = ¹₃ x 60 = 20 min
2¹₃ h = 2 h 20 min

Time that Luis left City G:
2 h 20 min before 1.00 p.m. = 10.40 a.m.

(b)
Remaining distance that they had to cover to reach City H
= 490 - 210
= 280 km

Duration that Luis had to travel before reaching City H
= 280 ÷ 90
= 3¹₉ h

Duration that Tom had to travel before reaching City H
= 280 ÷ 70
= 4 h

Duration that Tom took to arrive later than Luis in City H
= 4 - 3¹₉
= ⁸₉ h

Answer(s): (a) 10.40 a.m.; (b) ⁸₉ h