Japheth and Caden started on a 50-km cycling trip at the same time. They cycled at the same speed for first 5 km. For the remaining 45 km, Japheth cycled faster than Caden. He arrived at the finishing point 20 minutes before Caden who was 5 km behind him. Caden did not change his speed throughout and completed it at 08 30.

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

(a)
60 min = 1 h
20 min =²⁰₆₀ h = ¹₃ 

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

Time that Caden took for the trip
= 50 ÷ 15
= 3⁵₁₅ h
= 3¹₃ h
= 3 h 20 min

3 h 20 min before 08 30 is 05 10.

(b)
To find the time that Japheth took for the remaining 45 km of the trip, we need to use the time that Caden took subtract that of the time taken for first 5 km and the time that Japheth was faster than Caden.

Time that Japheth took for the remaining 45 km of the trip
= 3¹₃ - ¹₃ - ¹₃
= 2²₃ h

Japheth's average speed
= 45 ÷ 2²₃
= 16⁷₈ km/h

Answer(s): (a) 05 10; (b) 16⁷₈ km/h