David and Harry 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, David cycled faster than Harry. He arrived at the finishing point 24 minutes before Harry who was 10 km behind him. Harry did not change his speed throughout and completed it at 07 25.

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

(a)
60 min = 1 h
24 min =²⁴₆₀ h = ²₅ 

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

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

2 h 12 min before 07 25 is 05 13.

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

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

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

Answer(s): (a) 05 13; (b) 32¹₇ km/h