Archie and Luke 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, Archie cycled faster than Luke. He arrived at the finishing point 24 minutes before Luke who was 10 km behind him. Luke did not change his speed throughout and completed it at 08 25.

1. At what time did the trip begin? Give the answer in 12-hour format.
2. What was Archie's average speed for the remaining 45 km of the trip in km/h?

(a)
60 min = 1 h
24 min =²⁴₆₀ h = ²₅ 

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

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

2 h 12 min before 08 25 is 06 13.

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

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

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

Answer(s): (a) 06 13; (b) 32¹₇ km/h