City S and City T is 490 km apart. Harry left City S for City T at 9.00 a.m. travelling at an average speed of 70 km/h. Tim left City S later than Harry and caught up with him at 12.00 p.m. Tim was travelling at a speed of 84 km/h.

1. At what time did Tim leave City S?
2. How much later did Harry arrive in City T than Tim? 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 Harry covered when Tim caught up with Harry
= 3 x 70
= 210 km

Time that Tim took to travel 210 km
= 210 ÷ 84
= 2¹₂ h

1 h = 60 min
¹₂ h = ¹₂ x 60 = 30 min
2¹₂ h = 2 h 30 min

Time that Tim left City S:
2 h 30 min before 12.00 p.m. = 9.30 a.m.

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

Duration that Tim had to travel before reaching City T
= 280 ÷ 84
= 3¹₃ h

Duration that Harry had to travel before reaching City T
= 280 ÷ 70
= 4 h

Duration that Harry took to arrive later than Tim in City T
= 4 - 3¹₃
= ²₃ h

Answer(s): (a) 9.30 a.m.; (b) ²₃ h