Luis and Asher 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, Luis cycled faster than Asher. He arrived at the finishing point 24 minutes before Asher who was 10 km behind him. Asher did not change his speed throughout and completed it at 08 30.

1. At what time did the trip begin? Give the answer in 12-hour format.
2. What was Luis's average speed for the remaining 45 km of the trip in km/h?

(a)
60 min = 1 h
24 min =²⁴₆₀ h = ²₅ 

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

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

2 h 12 min before 08 30 is 06 18.

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

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

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

Answer(s): (a) 06 18; (b) 32¹₇ km/h