After cycling for 23 km, Luis took a break before he continued cycling ¹₇ of the remaining distance. He then realised that he still had ¹₅ of the total distance not completed. If Luis's average speed was 20 km/h, how much time did he take to complete the entire ride? Express your answer in mixed number.
Fraction of the remaining distance to cycle after resting
= 1 - ¹₇ 
= ⁶₇

⁶₇ of the remaining distance = ¹₅ of the total distance
⁶₇ of the remaining distance = ⁶₃₀ of the total distance

Total distance = 30 u

30 u - 6 u = 1 u + 23
24 u - 1 u = 23
23 u = 23
1 u = 23 ÷ 23 = 1

Total distance
= 30 x 1
= 30 km

Time taken by Luis to travel the entire distance
= 30 ÷ 20
= 1 ¹⁰₂₀
= 1¹₂ h

Answer(s): 1¹₂ h