After 40 minutes into a race, Sam has run ⁸₁₁ of the route while Eric has covered only ²₁₁ of the distance. Sam runs at the same average speed throughout the race and Eric’s average speed is 93 m/min slower than Sam’s. If Eric 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 Eric in first 40 min
= 40 x 93
= 3720 m

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

⁶₁₁ of the entire distance = 3720 m
¹₁₁ of the entire distance = 3720 ÷ 6 = 620 m

Distance that Eric ran in the first 40 min
= 2 x 620
= 1240 m

Eric's average speed
= 1240 ÷ 40
= 31 m/min

Sam's average speed
= 31 + 93
= 124 m/min

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

¹₁₁ of the entire distance = 620 m
³₁₁ of the entire distance = 3 x 620 = 1860 m

Duration that Sam would take to complete
= 1860 ÷ 124
= 15 min

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

⁹₁₁ of the entire distance = 9 x 620 = 5580 m  

Speed that Eric needs to take to complete distance at the same time as Sam
= 5580 ÷ 15
= 372 m/min

Increase in Eric's average speed
= 372 - 31
= 341 m/min

Percentage increase in Eric's average speed
= ³⁴¹₃₁ x 100%
≈ 1100%

Answer(s): 1100%