Howard and Luis started on a 45-km cycling trip at the same time. They cycled at the same speed for first 10 km. For the remaining 35 km, Howard cycled faster than Luis. He arrived at the finishing point 30 minutes before Luis who was 10 km behind him. Luis did not change his speed throughout and completed it at 07 25.

1. At what time did the trip begin? Give the answer in 12-hour format.
2. What was Howard's average speed for the remaining 35 km of the trip in km/h?

(a)
60 min = 1 h
30 min =³⁰₆₀ h = ¹₂ 

Luis's average speed
= 10 ÷ ¹₂
= 20 km/h

Time that Luis took for the trip
= 45 ÷ 20
= 2⁵₂₀ h
= 2¹₄ h
= 2 h 15 min

2 h 15 min before 07 25 is 05 10.

(b)
To find the time that Howard took for the remaining 35 km of the trip, we need to use the time that Luis took subtract that of the time taken for first 10 km and the time that Howard was faster than Luis.

Time that Howard took for the remaining 35 km of the trip
= 2¹₄ - ¹₂ - ¹₂
= 1¹₄ h

Howard's average speed
= 35 ÷ 1¹₄
= 28 km/h

Answer(s): (a) 05 10; (b) 28 km/h