Luis and Riordan started on a 48-km cycling trip at the same time. They cycled at the same speed for first 5 km. For the remaining 43 km, Luis cycled faster than Riordan. He arrived at the finishing point 20 minutes before Riordan who was 5 km behind him. Riordan did not change his speed throughout and completed it at 08 25.

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 43 km of the trip in km/h?

(a)
60 min = 1 h
20 min =²⁰₆₀ h = ¹₃ 

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

Time that Riordan took for the trip
= 48 ÷ 15
= 3³₁₅ h
= 3¹₅ h
= 3 h 12 min

3 h 12 min before 08 25 is 05 13.

(b)
To find the time that Luis took for the remaining 43 km of the trip, we need to use the time that Riordan took subtract that of the time taken for first 5 km and the time that Luis was faster than Riordan.

Time that Luis took for the remaining 43 km of the trip
= 3¹₅ - ¹₃ - ¹₃
= 2⁸₁₅ h

Luis's average speed
= 43 ÷ 2⁸₁₅
= 16³⁷₃₈ km/h

Answer(s): (a) 05 13; (b) 16³⁷₃₈ km/h