City S and City T is 450 km apart. Ken left City S for City T at 11.00 a.m. travelling at an average speed of 75 km/h. Daniel left City S later than Ken and caught up with him at 2.00 p.m. Daniel was travelling at a speed of 90 km/h.

1. At what time did Daniel leave City S?
2. How much later did Ken arrive in City T than Daniel? 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 Ken covered when Daniel caught up with Ken
= 3 x 75
= 225 km

Time that Daniel took to travel 225 km
= 225 ÷ 90
= 2¹₂ h

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

Time that Daniel left City S:
2 h 30 min before 2.00 p.m. = 11.30 a.m.

(b)
Remaining distance that they had to cover to reach City T
= 450 - 225
= 225 km

Duration that Daniel had to travel before reaching City T
= 225 ÷ 90
= 2¹₂ h

Duration that Ken had to travel before reaching City T
= 225 ÷ 75
= 3 h

Duration that Ken took to arrive later than Daniel in City T
= 3 - 2¹₂
= ¹₂ h

Answer(s): (a) 11.30 a.m.; (b) ¹₂ h