After cycling for 22 km, Fred 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 Fred's average speed was 28 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 + 22
12 u - 1 u = 22
11 u = 22
1 u = 22 ÷ 11 = 2

Total distance
= 15 x 2
= 30 km

Time taken by Fred to travel the entire distance
= 30 ÷ 28
= 1 ²₂₈
= 1¹₁₄ h

Answer(s): 1¹₁₄ h