Carl and Jack started on a 35-km cycling trip at the same time. They cycled at the same speed for first 5 km. For the remaining 30 km, Carl cycled faster than Jack. He arrived at the finishing point 20 minutes before Jack who was 5 km behind him. Jack 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 Carl's average speed for the remaining 30 km of the trip in km/h?

(a)
60 min = 1 h
20 min =²⁰₆₀ h = ¹₃ 

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

Time that Jack took for the trip
= 35 ÷ 15
= 2⁵₁₅ h
= 2¹₃ h
= 2 h 20 min

2 h 20 min before 09 30 is 07 10.

(b)
To find the time that Carl took for the remaining 30 km of the trip, we need to use the time that Jack took subtract that of the time taken for first 5 km and the time that Carl was faster than Jack.

Time that Carl took for the remaining 30 km of the trip
= 2¹₃ - ¹₃ - ¹₃
= 1²₃ h

Carl's average speed
= 30 ÷ 1²₃
= 18 km/h

Answer(s): (a) 07 10; (b) 18 km/h