After 25 minutes into a race, Liam has run ⁵₁₁ of the route while Pierre has covered only ³₁₁ of the distance. Liam runs at the same average speed throughout the race and Pierre’s average speed is 96 m/min slower than Liam’s. If Pierre wants to finish the race at the same time as Liam, 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 Liam ran more than Pierre in first 25 min
= 25 x 96
= 2400 m

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

²₁₁ of the entire distance = 2400 m
¹₁₁ of the entire distance = 2400 ÷ 2 = 1200 m

Distance that Pierre ran in the first 25 min
= 3 x 1200
= 3600 m

Pierre's average speed
= 3600 ÷ 25
= 144 m/min

Liam's average speed
= 144 + 96
= 240 m/min

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

¹₁₁ of the entire distance = 1200 m
⁶₁₁ of the entire distance = 6 x 1200 = 7200 m

Duration that Liam would take to complete
= 7200 ÷ 240
= 30 min

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

⁸₁₁ of the entire distance = 8 x 1200 = 9600 m  

Speed that Pierre needs to take to complete distance at the same time as Liam
= 9600 ÷ 30
= 320 m/min

Increase in Pierre's average speed
= 320 - 144
= 176 m/min

Percentage increase in Pierre's average speed
= ¹⁷⁶₁₄₄ x 100%
≈ 122%

Answer(s): 122%