Ben and Owen started on a 35-km cycling trip at the same time. They cycled at the same speed for first 5 km. For the remaining 30 km, Ben cycled faster than Owen. He arrived at the finishing point 20 minutes before Owen who was 5 km behind him. Owen 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 Ben's average speed for the remaining 30 km of the trip in km/h?

(a)
60 min = 1 h
20 min =²⁰₆₀ h = ¹₃ 

Owen's average speed
= 5 ÷ ¹₃
= 15 km/h

Time that Owen took for the trip
= 35 ÷ 15
= 2⁵₁₅ h
= 2¹₃ h
= 2 h 20 min

2 h 20 min before 09 30 is 07 10.

(b)
To find the time that Ben took for the remaining 30 km of the trip, we need to use the time that Owen took subtract that of the time taken for first 5 km and the time that Ben was faster than Owen.

Time that Ben took for the remaining 30 km of the trip
= 2¹₃ - ¹₃ - ¹₃
= 1²₃ h

Ben's average speed
= 30 ÷ 1²₃
= 18 km/h

Answer(s): (a) 07 10; (b) 18 km/h