George and Ben started on a 55-km cycling trip at the same time. They cycled at the same speed for first 10 km. For the remaining 45 km, George cycled faster than Ben. He arrived at the finishing point 24 minutes before Ben who was 10 km behind him. Ben did not change his speed throughout and completed it at 07 30.

1. At what time did the trip begin? Give the answer in 12-hour format.
2. What was George's average speed for the remaining 45 km of the trip in km/h?

(a)
60 min = 1 h
24 min =²⁴₆₀ h = ²₅ 

Ben's average speed
= 10 ÷ ²₅
= 25 km/h

Time that Ben took for the trip
= 55 ÷ 25
= 2⁵₂₅ h
= 2¹₅ h
= 2 h 12 min

2 h 12 min before 07 30 is 05 18.

(b)
To find the time that George took for the remaining 45 km of the trip, we need to use the time that Ben took subtract that of the time taken for first 10 km and the time that George was faster than Ben.

Time that George took for the remaining 45 km of the trip
= 2¹₅ - ²₅ - ²₅
= 1²₅ h

George's average speed
= 45 ÷ 1²₅
= 32¹₇ km/h

Answer(s): (a) 05 18; (b) 32¹₇ km/h