After 35 minutes into a race, Vincent has run ⁷₁₃ of the route while Perry has covered only ⁴₁₃ of the distance. Vincent runs at the same average speed throughout the race and Perry’s average speed is 96 m/min slower than Vincent’s. If Perry wants to finish the race at the same time as Vincent, 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 Vincent ran more than Perry in first 35 min
= 35 x 96
= 3360 m

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

³₁₃ of the entire distance = 3360 m
¹₁₃ of the entire distance = 3360 ÷ 3 = 1120 m

Distance that Perry ran in the first 35 min
= 4 x 1120
= 4480 m

Perry's average speed
= 4480 ÷ 35
= 128 m/min

Vincent's average speed
= 128 + 96
= 224 m/min

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

¹₁₃ of the entire distance = 1120 m
⁶₁₃ of the entire distance = 6 x 1120 = 6720 m

Duration that Vincent would take to complete
= 6720 ÷ 224
= 30 min

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

⁹₁₃ of the entire distance = 9 x 1120 = 10080 m  

Speed that Perry needs to take to complete distance at the same time as Vincent
= 10080 ÷ 30
= 336 m/min

Increase in Perry's average speed
= 336 - 128
= 208 m/min

Percentage increase in Perry's average speed
= ²⁰⁸₁₂₈ x 100%
≈ 163%

Answer(s): 163%