City Q and City R is 666 km apart. Luis left City Q for City R at 11.00 a.m. travelling at an average speed of 74 km/h. Ahmad left City Q later than Luis and caught up with him at 3.00 p.m. Ahmad was travelling at a speed of 111 km/h.

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

(a)
From 11.00 a.m. to 3.00 p.m. = 4 h

Distance that Luis covered when Ahmad caught up with Luis
= 4 x 74
= 296 km

Time that Ahmad took to travel 296 km
= 296 ÷ 111
= 2²₃ h

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

Time that Ahmad left City Q:
2 h 40 min before 3.00 p.m. = 12.20 p.m.

(b)
Remaining distance that they had to cover to reach City R
= 666 - 296
= 370 km

Duration that Ahmad had to travel before reaching City R
= 370 ÷ 111
= 3¹₃ h

Duration that Luis had to travel before reaching City R
= 370 ÷ 74
= 5 h

Duration that Luis took to arrive later than Ahmad in City R
= 5 - 3¹₃
= 1²₃ h

Answer(s): (a) 12.20 p.m.; (b) 1²₃ h