Ivan and Glen 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, Ivan cycled faster than Glen. He arrived at the finishing point 20 minutes before Glen who was 5 km behind him. Glen 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 Ivan's average speed for the remaining 30 km of the trip in km/h?

(a)
60 min = 1 h
20 min =²⁰₆₀ h = ¹₃ 

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

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

2 h 20 min before 07 30 is 05 10.

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

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

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

Answer(s): (a) 05 10; (b) 18 km/h