Valen and Nick started on a 45-km cycling trip at the same time. They cycled at the same speed for first 10 km. For the remaining 35 km, Valen cycled faster than Nick. He arrived at the finishing point 30 minutes before Nick who was 10 km behind him. Nick did not change his speed throughout and completed it at 07 30.

1. At what time did the trip begin? Give the answer in 12-hour format.
2. What was Valen's average speed for the remaining 35 km of the trip in km/h?

(a)
60 min = 1 h
30 min =³⁰₆₀ h = ¹₂ 

Nick's average speed
= 10 ÷ ¹₂
= 20 km/h

Time that Nick took for the trip
= 45 ÷ 20
= 2⁵₂₀ h
= 2¹₄ h
= 2 h 15 min

2 h 15 min before 07 30 is 05 15.

(b)
To find the time that Valen took for the remaining 35 km of the trip, we need to use the time that Nick took subtract that of the time taken for first 10 km and the time that Valen was faster than Nick.

Time that Valen took for the remaining 35 km of the trip
= 2¹₄ - ¹₂ - ¹₂
= 1¹₄ h

Valen's average speed
= 35 ÷ 1¹₄
= 28 km/h

Answer(s): (a) 05 15; (b) 28 km/h