Warren and Archie 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, Warren cycled faster than Archie. He arrived at the finishing point 40 minutes before Archie who was 10 km behind him. Archie 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 Warren's average speed for the remaining 38 km of the trip in km/h?

(a)
60 min = 1 h
40 min =⁴⁰₆₀ h = ²₃ 

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

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

3 h 12 min before 08 30 is 05 18.

(b)
To find the time that Warren took for the remaining 38 km of the trip, we need to use the time that Archie took subtract that of the time taken for first 10 km and the time that Warren was faster than Archie.

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

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

Answer(s): (a) 05 18; (b) 20⁵₁₄ km/h