Carl and Tommy started on a 55-km cycling trip at the same time. They cycled at the same speed for first 5 km. For the remaining 50 km, Carl cycled faster than Tommy. He arrived at the finishing point 12 minutes before Tommy who was 5 km behind him. Tommy 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 50 km of the trip in km/h?

(a)
60 min = 1 h
12 min =¹²₆₀ h = ¹₅ 

Tommy's average speed
= 5 ÷ ¹₅
= 25 km/h

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

2 h 12 min before 09 30 is 07 18.

(b)
To find the time that Carl took for the remaining 50 km of the trip, we need to use the time that Tommy took subtract that of the time taken for first 5 km and the time that Carl was faster than Tommy.

Time that Carl took for the remaining 50 km of the trip
= 2¹₅ - ¹₅ - ¹₅
= 1⁴₅ h

Carl's average speed
= 50 ÷ 1⁴₅
= 27⁷₉ km/h

Answer(s): (a) 07 18; (b) 27⁷₉ km/h