Billy and Archie started on a 50-km cycling trip at the same time. They cycled at the same speed for first 5 km. For the remaining 45 km, Billy cycled faster than Archie. He arrived at the finishing point 20 minutes before Archie who was 5 km behind him. Archie 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 Billy's average speed for the remaining 45 km of the trip in km/h?

(a)
60 min = 1 h
20 min =²⁰₆₀ h = ¹₃ 

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

Time that Archie took for the trip
= 50 ÷ 15
= 3⁵₁₅ h
= 3¹₃ h
= 3 h 20 min

3 h 20 min before 07 30 is 04 10.

(b)
To find the time that Billy took for the remaining 45 km of the trip, we need to use the time that Archie took subtract that of the time taken for first 5 km and the time that Billy was faster than Archie.

Time that Billy took for the remaining 45 km of the trip
= 3¹₃ - ¹₃ - ¹₃
= 2²₃ h

Billy's average speed
= 45 ÷ 2²₃
= 16⁷₈ km/h

Answer(s): (a) 04 10; (b) 16⁷₈ km/h