After 40 minutes into a race, John has run ⁸₁₁ of the route while Dylan has covered only ²₁₁ of the distance. John runs at the same average speed throughout the race and Dylan’s average speed is 78 m/min slower than John’s. If Dylan wants to finish the race at the same time as John, 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 John ran more than Dylan in first 40 min
= 40 x 78
= 3120 m

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

⁶₁₁ of the entire distance = 3120 m
¹₁₁ of the entire distance = 3120 ÷ 6 = 520 m

Distance that Dylan ran in the first 40 min
= 2 x 520
= 1040 m

Dylan's average speed
= 1040 ÷ 40
= 26 m/min

John's average speed
= 26 + 78
= 104 m/min

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

¹₁₁ of the entire distance = 520 m
³₁₁ of the entire distance = 3 x 520 = 1560 m

Duration that John would take to complete
= 1560 ÷ 104
= 15 min

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

⁹₁₁ of the entire distance = 9 x 520 = 4680 m  

Speed that Dylan needs to take to complete distance at the same time as John
= 4680 ÷ 15
= 312 m/min

Increase in Dylan's average speed
= 312 - 26
= 286 m/min

Percentage increase in Dylan's average speed
= ²⁸⁶₂₆ x 100%
≈ 1100%

Answer(s): 1100%