Julian and Bobby 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, Julian cycled faster than Bobby. He arrived at the finishing point 12 minutes before Bobby who was 5 km behind him. Bobby did not change his speed throughout and completed it at 09 25.

1. At what time did the trip begin? Give the answer in 12-hour format.
2. What was Julian's average speed for the remaining 50 km of the trip in km/h?

(a)
60 min = 1 h
12 min =¹²₆₀ h = ¹₅ 

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

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

2 h 12 min before 09 25 is 07 13.

(b)
To find the time that Julian took for the remaining 50 km of the trip, we need to use the time that Bobby took subtract that of the time taken for first 5 km and the time that Julian was faster than Bobby.

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

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

Answer(s): (a) 07 13; (b) 27⁷₉ km/h