After 40 minutes into a race, Sam has run ⁵₁₁ of the route while Michael has covered only ²₁₁ of the distance. Sam runs at the same average speed throughout the race and Michael’s average speed is 60 m/min slower than Sam’s. If Michael wants to finish the race at the same time as Sam, 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 Sam ran more than Michael in first 40 min
= 40 x 60
= 2400 m

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

³₁₁ of the entire distance = 2400 m
¹₁₁ of the entire distance = 2400 ÷ 3 = 800 m

Distance that Michael ran in the first 40 min
= 2 x 800
= 1600 m

Michael's average speed
= 1600 ÷ 40
= 40 m/min

Sam's average speed
= 40 + 60
= 100 m/min

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

¹₁₁ of the entire distance = 800 m
⁶₁₁ of the entire distance = 6 x 800 = 4800 m

Duration that Sam would take to complete
= 4800 ÷ 100
= 48 min

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

⁹₁₁ of the entire distance = 9 x 800 = 7200 m  

Speed that Michael needs to take to complete distance at the same time as Sam
= 7200 ÷ 48
= 150 m/min

Increase in Michael's average speed
= 150 - 40
= 110 m/min

Percentage increase in Michael's average speed
= ¹¹⁰₄₀ x 100%
≈ 275%

Answer(s): 275%