After 25 minutes into a race, Zane has run ⁵₁₁ of the route while Wesley has covered only ²₁₁ of the distance. Zane runs at the same average speed throughout the race and Wesley’s average speed is 54 m/min slower than Zane’s. If Wesley wants to finish the race at the same time as Zane, 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 Zane ran more than Wesley in first 25 min
= 25 x 54
= 1350 m

Fraction of the entire distance that was covered by Zane more than Wesley in the first 25 min
= ⁵₁₁ - ²₁₁
= ³₁₁

³₁₁ of the entire distance = 1350 m
¹₁₁ of the entire distance = 1350 ÷ 3 = 450 m

Distance that Wesley ran in the first 25 min
= 2 x 450
= 900 m

Wesley's average speed
= 900 ÷ 25
= 36 m/min

Zane's average speed
= 36 + 54
= 90 m/min

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

¹₁₁ of the entire distance = 450 m
⁶₁₁ of the entire distance = 6 x 450 = 2700 m

Duration that Zane would take to complete
= 2700 ÷ 90
= 30 min

Fraction of the journey that Zane needed to run to complete the race
= 1 - ²₁₁
= ⁹₁₁

⁹₁₁ of the entire distance = 9 x 450 = 4050 m  

Speed that Wesley needs to take to complete distance at the same time as Zane
= 4050 ÷ 30
= 135 m/min

Increase in Wesley's average speed
= 135 - 36
= 99 m/min

Percentage increase in Wesley's average speed
= ⁹⁹₃₆ x 100%
≈ 275%

Answer(s): 275%