Zeph and Ethan started on a 55-km cycling trip at the same time. They cycled at the same speed for first 10 km. For the remaining 45 km, Zeph cycled faster than Ethan. He arrived at the finishing point 24 minutes before Ethan who was 10 km behind him. Ethan 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 Zeph's average speed for the remaining 45 km of the trip in km/h?

(a)
60 min = 1 h
24 min =²⁴₆₀ h = ²₅ 

Ethan's average speed
= 10 ÷ ²₅
= 25 km/h

Time that Ethan took for the trip
= 55 ÷ 25
= 2⁵₂₅ h
= 2¹₅ h
= 2 h 12 min

2 h 12 min before 09 25 is 07 13.

(b)
To find the time that Zeph took for the remaining 45 km of the trip, we need to use the time that Ethan took subtract that of the time taken for first 10 km and the time that Zeph was faster than Ethan.

Time that Zeph took for the remaining 45 km of the trip
= 2¹₅ - ²₅ - ²₅
= 1²₅ h

Zeph's average speed
= 45 ÷ 1²₅
= 32¹₇ km/h

Answer(s): (a) 07 13; (b) 32¹₇ km/h