Billy and Jenson 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, Billy cycled faster than Jenson. He arrived at the finishing point 30 minutes before Jenson who was 10 km behind him. Jenson did not change his speed throughout and completed it at 09 30.

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

(a)
60 min = 1 h
30 min =³⁰₆₀ h = ¹₂ 

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

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

2 h 15 min before 09 30 is 07 15.

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

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

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

Answer(s): (a) 07 15; (b) 28 km/h