City Q and City R is 520 km apart. Perry left City Q for City R at 7.00 a.m. travelling at an average speed of 65 km/h. Ken left City Q later than Perry and caught up with him at 10.00 a.m. Ken was travelling at a speed of 117 km/h.

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

(a)
From 7.00 a.m. to 10.00 a.m. = 3 h

Distance that Perry covered when Ken caught up with Perry
= 3 x 65
= 195 km

Time that Ken took to travel 195 km
= 195 ÷ 117
= 1²₃ h

1 h = 60 min
²₃ h = ²₃ x 60 = 40 min
1²₃ h = 1 h 40 min

Time that Ken left City Q:
1 h 40 min before 10.00 a.m. = 8.20 a.m.

(b)
Remaining distance that they had to cover to reach City R
= 520 - 195
= 325 km

Duration that Ken had to travel before reaching City R
= 325 ÷ 117
= 2⁷₉ h

Duration that Perry had to travel before reaching City R
= 325 ÷ 65
= 5 h

Duration that Perry took to arrive later than Ken in City R
= 5 - 2⁷₉
= 2²₉ h

Answer(s): (a) 8.20 a.m.; (b) 2²₉ h