After cycling for 27 km, Luke took a break before he continued cycling ¹₅ of the remaining distance. He then realised that he still had ¹₈ of the total distance not completed. If Luke's average speed was 26 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 - ¹₅ 
= ⁴₅

⁴₅ of the remaining distance = ¹₈ of the total distance
⁴₅ of the remaining distance = ⁴₃₂ of the total distance

Total distance = 32 u

32 u - 4 u = 1 u + 27
28 u - 1 u = 27
27 u = 27
1 u = 27 ÷ 27 = 1

Total distance
= 32 x 1
= 32 km

Time taken by Luke to travel the entire distance
= 32 ÷ 26
= 1 ⁶₂₆
= 1³₁₃ h

Answer(s): 1³₁₃ h