After 40 minutes into a race, Will has run ⁵₁₁ of the route while Ivan has covered only ³₁₁ of the distance. Will runs at the same average speed throughout the race and Ivan’s average speed is 72 m/min slower than Will’s. If Ivan 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 Ivan in first 40 min
= 40 x 72
= 2880 m

Fraction of the entire distance that was covered by Will more than Ivan in the first 40 min
= ⁵₁₁ - ³₁₁
= ²₁₁

²₁₁ of the entire distance = 2880 m
¹₁₁ of the entire distance = 2880 ÷ 2 = 1440 m

Distance that Ivan ran in the first 40 min
= 3 x 1440
= 4320 m

Ivan's average speed
= 4320 ÷ 40
= 108 m/min

Will's average speed
= 108 + 72
= 180 m/min

Fraction of the journey that Will needed to run to complete the race
= 1 - ⁵₁₁
= ⁶₁₁

¹₁₁ of the entire distance = 1440 m
⁶₁₁ of the entire distance = 6 x 1440 = 8640 m

Duration that Will would take to complete
= 8640 ÷ 180
= 48 min

Fraction of the journey that Will needed to run to complete the race
= 1 - ³₁₁
= ⁸₁₁

⁸₁₁ of the entire distance = 8 x 1440 = 11520 m  

Speed that Ivan needs to take to complete distance at the same time as Will
= 11520 ÷ 48
= 240 m/min

Increase in Ivan's average speed
= 240 - 108
= 132 m/min

Percentage increase in Ivan's average speed
= ¹³²₁₀₈ x 100%
≈ 122%

Answer(s): 122%