Caden and Fred started on a 48-km cycling trip at the same time. They cycled at the same speed for first 10 km. For the remaining 38 km, Caden cycled faster than Fred. He arrived at the finishing point 40 minutes before Fred who was 10 km behind him. Fred did not change his speed throughout and completed it at 09 30.

1. At what time did the trip begin? Give the answer in 12-hour format.
2. What was Caden's average speed for the remaining 38 km of the trip in km/h?

(a)
60 min = 1 h
40 min =⁴⁰₆₀ h = ²₃ 

Fred's average speed
= 10 ÷ ²₃
= 15 km/h

Time that Fred took for the trip
= 48 ÷ 15
= 3³₁₅ h
= 3¹₅ h
= 3 h 12 min

3 h 12 min before 09 30 is 06 18.

(b)
To find the time that Caden took for the remaining 38 km of the trip, we need to use the time that Fred took subtract that of the time taken for first 10 km and the time that Caden was faster than Fred.

Time that Caden took for the remaining 38 km of the trip
= 3¹₅ - ²₃ - ²₃
= 1¹³₁₅ h

Caden's average speed
= 38 ÷ 1¹³₁₅
= 20⁵₁₄ km/h

Answer(s): (a) 06 18; (b) 20⁵₁₄ km/h