David and Gabriel started on a 35-km cycling trip at the same time. They cycled at the same speed for first 5 km. For the remaining 30 km, David cycled faster than Gabriel. He arrived at the finishing point 20 minutes before Gabriel who was 5 km behind him. Gabriel 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 David's average speed for the remaining 30 km of the trip in km/h?

(a)
60 min = 1 h
20 min =²⁰₆₀ h = ¹₃ 

Gabriel's average speed
= 5 ÷ ¹₃
= 15 km/h

Time that Gabriel took for the trip
= 35 ÷ 15
= 2⁵₁₅ h
= 2¹₃ h
= 2 h 20 min

2 h 20 min before 07 30 is 05 10.

(b)
To find the time that David took for the remaining 30 km of the trip, we need to use the time that Gabriel took subtract that of the time taken for first 5 km and the time that David was faster than Gabriel.

Time that David took for the remaining 30 km of the trip
= 2¹₃ - ¹₃ - ¹₃
= 1²₃ h

David's average speed
= 30 ÷ 1²₃
= 18 km/h

Answer(s): (a) 05 10; (b) 18 km/h