City Q and City R is 539 km apart. Vincent left City Q for City R at 9.00 a.m. travelling at an average speed of 77 km/h. Justin left City Q later than Vincent and caught up with him at 11.00 a.m. Justin was travelling at a speed of 88 km/h.

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

(a)
From 9.00 a.m. to 11.00 a.m. = 2 h

Distance that Vincent covered when Justin caught up with Vincent
= 2 x 77
= 154 km

Time that Justin took to travel 154 km
= 154 ÷ 88
= 1³₄ h

1 h = 60 min
³₄ h = ³₄ x 60 = 45 min
1³₄ h = 1 h 45 min

Time that Justin left City Q:
1 h 45 min before 11.00 a.m. = 9.15 a.m.

(b)
Remaining distance that they had to cover to reach City R
= 539 - 154
= 385 km

Duration that Justin had to travel before reaching City R
= 385 ÷ 88
= 4³₈ h

Duration that Vincent had to travel before reaching City R
= 385 ÷ 77
= 5 h

Duration that Vincent took to arrive later than Justin in City R
= 5 - 4³₈
= ⁵₈ h

Answer(s): (a) 9.15 a.m.; (b) ⁵₈ h