After 40 minutes into a race, Pierre has run ⁵₁₁ of the route while Michael has covered only ²₁₁ of the distance. Pierre runs at the same average speed throughout the race and Michael’s average speed is 72 m/min slower than Pierre’s. If Michael wants to finish the race at the same time as Pierre, 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 Pierre ran more than Michael in first 40 min
= 40 x 72
= 2880 m

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

³₁₁ of the entire distance = 2880 m
¹₁₁ of the entire distance = 2880 ÷ 3 = 960 m

Distance that Michael ran in the first 40 min
= 2 x 960
= 1920 m

Michael's average speed
= 1920 ÷ 40
= 48 m/min

Pierre's average speed
= 48 + 72
= 120 m/min

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

¹₁₁ of the entire distance = 960 m
⁶₁₁ of the entire distance = 6 x 960 = 5760 m

Duration that Pierre would take to complete
= 5760 ÷ 120
= 48 min

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

⁹₁₁ of the entire distance = 9 x 960 = 8640 m  

Speed that Michael needs to take to complete distance at the same time as Pierre
= 8640 ÷ 48
= 180 m/min

Increase in Michael's average speed
= 180 - 48
= 132 m/min

Percentage increase in Michael's average speed
= ¹³²₄₈ x 100%
≈ 275%

Answer(s): 275%