After cycling for 33 km, Billy took a break before he continued cycling ¹₄ of the remaining distance. He then realised that he still had ¹₅ of the total distance not completed. If Billy's average speed was 21 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 - ¹₄ 
= ³₄

³₄ of the remaining distance = ¹₅ of the total distance
³₄ of the remaining distance = ³₁₅ of the total distance

Total distance = 15 u

15 u - 3 u = 1 u + 33
12 u - 1 u = 33
11 u = 33
1 u = 33 ÷ 11 = 3

Total distance
= 15 x 3
= 45 km

Time taken by Billy to travel the entire distance
= 45 ÷ 21
= 2 ³₂₁
= 2¹₇ h

Answer(s): 2¹₇ h