City R and City S is 480 km apart. Vaidev left City R for City S at 9.00 a.m. travelling at an average speed of 80 km/h. Sam left City R later than Vaidev and caught up with him at 12.00 p.m. Sam was travelling at a speed of 90 km/h.

1. At what time did Sam leave City R?
2. How much later did Vaidev arrive in City S than Sam? 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 Vaidev covered when Sam caught up with Vaidev
= 3 x 80
= 240 km

Time that Sam took to travel 240 km
= 240 ÷ 90
= 2²₃ h

1 h = 60 min
²₃ h = ²₃ x 60 = 40 min
2²₃ h = 2 h 40 min

Time that Sam left City R:
2 h 40 min before 12.00 p.m. = 9.20 a.m.

(b)
Remaining distance that they had to cover to reach City S
= 480 - 240
= 240 km

Duration that Sam had to travel before reaching City S
= 240 ÷ 90
= 2²₃ h

Duration that Vaidev had to travel before reaching City S
= 240 ÷ 80
= 3 h

Duration that Vaidev took to arrive later than Sam in City S
= 3 - 2²₃
= ¹₃ h

Answer(s): (a) 9.20 a.m.; (b) ¹₃ h