Billy and Tim 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, Billy cycled faster than Tim. He arrived at the finishing point 24 minutes before Tim who was 10 km behind him. Tim did not change his speed throughout and completed it at 09 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
24 min =²⁴₆₀ h = ²₅ 

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

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

2 h 12 min before 09 30 is 07 18.

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

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

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

Answer(s): (a) 07 18; (b) 32¹₇ km/h