After 40 minutes into a race, Billy has run ⁸₁₁ of the route while Japheth has covered only ²₁₁ of the distance. Billy runs at the same average speed throughout the race and Japheth’s average speed is 99 m/min slower than Billy’s. If Japheth wants to finish the race at the same time as Billy, 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 Billy ran more than Japheth in first 40 min
= 40 x 99
= 3960 m

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

⁶₁₁ of the entire distance = 3960 m
¹₁₁ of the entire distance = 3960 ÷ 6 = 660 m

Distance that Japheth ran in the first 40 min
= 2 x 660
= 1320 m

Japheth's average speed
= 1320 ÷ 40
= 33 m/min

Billy's average speed
= 33 + 99
= 132 m/min

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

¹₁₁ of the entire distance = 660 m
³₁₁ of the entire distance = 3 x 660 = 1980 m

Duration that Billy would take to complete
= 1980 ÷ 132
= 15 min

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

⁹₁₁ of the entire distance = 9 x 660 = 5940 m  

Speed that Japheth needs to take to complete distance at the same time as Billy
= 5940 ÷ 15
= 396 m/min

Increase in Japheth's average speed
= 396 - 33
= 363 m/min

Percentage increase in Japheth's average speed
= ³⁶³₃₃ x 100%
≈ 1100%

Answer(s): 1100%