George and Neave 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, George cycled faster than Neave. He arrived at the finishing point 30 minutes before Neave who was 10 km behind him. Neave 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 George's average speed for the remaining 35 km of the trip in km/h?

(a)
60 min = 1 h
30 min =³⁰₆₀ h = ¹₂ 

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

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

2 h 15 min before 08 30 is 06 15.

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

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

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

Answer(s): (a) 06 15; (b) 28 km/h