After 25 minutes into a race, Sean has run ⁵₁₁ of the route while Wesley has covered only ³₁₁ of the distance. Sean runs at the same average speed throughout the race and Wesley’s average speed is 54 m/min slower than Sean’s. If Wesley wants to finish the race at the same time as Sean, 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 Sean ran more than Wesley in first 25 min
= 25 x 54
= 1350 m

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

²₁₁ of the entire distance = 1350 m
¹₁₁ of the entire distance = 1350 ÷ 2 = 675 m

Distance that Wesley ran in the first 25 min
= 3 x 675
= 2025 m

Wesley's average speed
= 2025 ÷ 25
= 81 m/min

Sean's average speed
= 81 + 54
= 135 m/min

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

¹₁₁ of the entire distance = 675 m
⁶₁₁ of the entire distance = 6 x 675 = 4050 m

Duration that Sean would take to complete
= 4050 ÷ 135
= 30 min

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

⁸₁₁ of the entire distance = 8 x 675 = 5400 m  

Speed that Wesley needs to take to complete distance at the same time as Sean
= 5400 ÷ 30
= 180 m/min

Increase in Wesley's average speed
= 180 - 81
= 99 m/min

Percentage increase in Wesley's average speed
= ⁹⁹₈₁ x 100%
≈ 122%

Answer(s): 122%