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

Fraction of the entire distance that was covered by Brandon more than Zane 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 Zane ran in the first 40 min
= 2 x 520
= 1040 m

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

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

Fraction of the journey that Brandon 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 Brandon would take to complete
= 1560 ÷ 104
= 15 min

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

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

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

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

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

Answer(s): 1100%