After 40 minutes into a race, Vincent has run ⁵₁₁ of the route while Ben has covered only ³₁₁ of the distance. Vincent runs at the same average speed throughout the race and Ben’s average speed is 90 m/min slower than Vincent’s. If Ben wants to finish the race at the same time as Vincent, 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 Vincent ran more than Ben in first 40 min
= 40 x 90
= 3600 m

Fraction of the entire distance that was covered by Vincent more than Ben in the first 40 min
= ⁵₁₁ - ³₁₁
= ²₁₁

²₁₁ of the entire distance = 3600 m
¹₁₁ of the entire distance = 3600 ÷ 2 = 1800 m

Distance that Ben ran in the first 40 min
= 3 x 1800
= 5400 m

Ben's average speed
= 5400 ÷ 40
= 135 m/min

Vincent's average speed
= 135 + 90
= 225 m/min

Fraction of the journey that Vincent needed to run to complete the race
= 1 - ⁵₁₁
= ⁶₁₁

¹₁₁ of the entire distance = 1800 m
⁶₁₁ of the entire distance = 6 x 1800 = 10800 m

Duration that Vincent would take to complete
= 10800 ÷ 225
= 48 min

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

⁸₁₁ of the entire distance = 8 x 1800 = 14400 m  

Speed that Ben needs to take to complete distance at the same time as Vincent
= 14400 ÷ 48
= 300 m/min

Increase in Ben's average speed
= 300 - 135
= 165 m/min

Percentage increase in Ben's average speed
= ¹⁶⁵₁₃₅ x 100%
≈ 122%

Answer(s): 122%