Ian and Ivan 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, Ian cycled faster than Ivan. He arrived at the finishing point 30 minutes before Ivan who was 10 km behind him. Ivan did not change his speed throughout and completed it at 09 25.

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

(a)
60 min = 1 h
30 min =³⁰₆₀ h = ¹₂ 

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

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

2 h 15 min before 09 25 is 07 10.

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

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

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

Answer(s): (a) 07 10; (b) 28 km/h