After 40 minutes into a race, Perry has run ⁸₁₁ of the route while Sam has covered only ²₁₁ of the distance. Perry runs at the same average speed throughout the race and Sam’s average speed is 63 m/min slower than Perry’s. If Sam wants to finish the race at the same time as Perry, 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 Perry ran more than Sam in first 40 min
= 40 x 63
= 2520 m

Fraction of the entire distance that was covered by Perry more than Sam in the first 40 min
= ⁸₁₁ - ²₁₁
= ⁶₁₁

⁶₁₁ of the entire distance = 2520 m
¹₁₁ of the entire distance = 2520 ÷ 6 = 420 m

Distance that Sam ran in the first 40 min
= 2 x 420
= 840 m

Sam's average speed
= 840 ÷ 40
= 21 m/min

Perry's average speed
= 21 + 63
= 84 m/min

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

¹₁₁ of the entire distance = 420 m
³₁₁ of the entire distance = 3 x 420 = 1260 m

Duration that Perry would take to complete
= 1260 ÷ 84
= 15 min

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

⁹₁₁ of the entire distance = 9 x 420 = 3780 m  

Speed that Sam needs to take to complete distance at the same time as Perry
= 3780 ÷ 15
= 252 m/min

Increase in Sam's average speed
= 252 - 21
= 231 m/min

Percentage increase in Sam's average speed
= ²³¹₂₁ x 100%
≈ 1100%

Answer(s): 1100%