After 35 minutes into a race, Will has run ⁷₁₃ of the route while Zeph has covered only ⁴₁₃ of the distance. Will runs at the same average speed throughout the race and Zeph’s average speed is 102 m/min slower than Will’s. If Zeph wants to finish the race at the same time as Will, 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 Will ran more than Zeph in first 35 min
= 35 x 102
= 3570 m

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

³₁₃ of the entire distance = 3570 m
¹₁₃ of the entire distance = 3570 ÷ 3 = 1190 m

Distance that Zeph ran in the first 35 min
= 4 x 1190
= 4760 m

Zeph's average speed
= 4760 ÷ 35
= 136 m/min

Will's average speed
= 136 + 102
= 238 m/min

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

¹₁₃ of the entire distance = 1190 m
⁶₁₃ of the entire distance = 6 x 1190 = 7140 m

Duration that Will would take to complete
= 7140 ÷ 238
= 30 min

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

⁹₁₃ of the entire distance = 9 x 1190 = 10710 m  

Speed that Zeph needs to take to complete distance at the same time as Will
= 10710 ÷ 30
= 357 m/min

Increase in Zeph's average speed
= 357 - 136
= 221 m/min

Percentage increase in Zeph's average speed
= ²²¹₁₃₆ x 100%
≈ 163%

Answer(s): 163%