City R and City S is 378 km apart. Rael left City R for City S at 8.00 a.m. travelling at an average speed of 63 km/h. Ahmad left City R later than Rael and caught up with him at 11.00 a.m. Ahmad was travelling at a speed of 81 km/h.

1. At what time did Ahmad leave City R?
2. How much later did Rael arrive in City S than Ahmad? Express your answer in h as a fraction or mixed number.

(a)
From 8.00 a.m. to 11.00 a.m. = 3 h

Distance that Rael covered when Ahmad caught up with Rael
= 3 x 63
= 189 km

Time that Ahmad took to travel 189 km
= 189 ÷ 81
= 2¹₃ h

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

Time that Ahmad left City R:
2 h 20 min before 11.00 a.m. = 8.40 a.m.

(b)
Remaining distance that they had to cover to reach City S
= 378 - 189
= 189 km

Duration that Ahmad had to travel before reaching City S
= 189 ÷ 81
= 2¹₃ h

Duration that Rael had to travel before reaching City S
= 189 ÷ 63
= 3 h

Duration that Rael took to arrive later than Ahmad in City S
= 3 - 2¹₃
= ²₃ h

Answer(s): (a) 8.40 a.m.; (b) ²₃ h