Justin and Bobby 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, Justin cycled faster than Bobby. He arrived at the finishing point 20 minutes before Bobby who was 5 km behind him. Bobby 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 Justin's average speed for the remaining 30 km of the trip in km/h?

(a)
60 min = 1 h
20 min =²⁰₆₀ h = ¹₃ 

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

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

2 h 20 min before 08 30 is 06 10.

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

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

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

Answer(s): (a) 06 10; (b) 18 km/h