After 35 minutes into a race, Albert has run ⁷₁₃ of the route while John has covered only ⁴₁₃ of the distance. Albert runs at the same average speed throughout the race and John’s average speed is 54 m/min slower than Albert’s. If John wants to finish the race at the same time as Albert, by how many percent should he increase his average speed by for the remaining part of the race? Round off your answer to the nearest whole number.
Extra distance that Albert ran more than John in first 35 min
= 35 x 54
= 1890 m

Fraction of the entire distance that was covered by Albert more than John in the first 35 min
= ⁷₁₃ - ⁴₁₃
= ³₁₃

³₁₃ of the entire distance = 1890 m
¹₁₃ of the entire distance = 1890 ÷ 3 = 630 m

Distance that John ran in the first 35 min
= 4 x 630
= 2520 m

John's average speed
= 2520 ÷ 35
= 72 m/min

Albert's average speed
= 72 + 54
= 126 m/min

Fraction of the journey that Albert needed to run to complete the race
= 1 - ⁷₁₃
= ⁶₁₃

¹₁₃ of the entire distance = 630 m
⁶₁₃ of the entire distance = 6 x 630 = 3780 m

Duration that Albert would take to complete
= 3780 ÷ 126
= 30 min

Fraction of the journey that Albert needed to run to complete the race
= 1 - ⁴₁₃
= ⁹₁₃

⁹₁₃ of the entire distance = 9 x 630 = 5670 m  

Speed that John needs to take to complete distance at the same time as Albert
= 5670 ÷ 30
= 189 m/min

Increase in John's average speed
= 189 - 72
= 117 m/min

Percentage increase in John's average speed
= ¹¹⁷₇₂ x 100%
≈ 163%

Answer(s): 163%