Simon and Sam started on a 48-km cycling trip at the same time. They cycled at the same speed for first 10 km. For the remaining 38 km, Simon cycled faster than Sam. He arrived at the finishing point 40 minutes before Sam who was 10 km behind him. Sam 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 Simon's average speed for the remaining 38 km of the trip in km/h?

(a)
60 min = 1 h
40 min =⁴⁰₆₀ h = ²₃ 

Sam's average speed
= 10 ÷ ²₃
= 15 km/h

Time that Sam 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 Simon took for the remaining 38 km of the trip, we need to use the time that Sam took subtract that of the time taken for first 10 km and the time that Simon was faster than Sam.

Time that Simon took for the remaining 38 km of the trip
= 3¹₅ - ²₃ - ²₃
= 1¹³₁₅ h

Simon's average speed
= 38 ÷ 1¹³₁₅
= 20⁵₁₄ km/h

Answer(s): (a) 05 13; (b) 20⁵₁₄ km/h