Dylan and Billy started on a 55-km cycling trip at the same time. They cycled at the same speed for first 5 km. For the remaining 50 km, Dylan cycled faster than Billy. He arrived at the finishing point 12 minutes before Billy who was 5 km behind him. Billy 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 Dylan's average speed for the remaining 50 km of the trip in km/h?

(a)
60 min = 1 h
12 min =¹²₆₀ h = ¹₅ 

Billy's average speed
= 5 ÷ ¹₅
= 25 km/h

Time that Billy 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 Dylan took for the remaining 50 km of the trip, we need to use the time that Billy took subtract that of the time taken for first 5 km and the time that Dylan was faster than Billy.

Time that Dylan took for the remaining 50 km of the trip
= 2¹₅ - ¹₅ - ¹₅
= 1⁴₅ h

Dylan's average speed
= 50 ÷ 1⁴₅
= 27⁷₉ km/h

Answer(s): (a) 05 18; (b) 27⁷₉ km/h