After 20 minutes into a race, David has run ⁵₁₁ of the route while Neave has covered only ³₁₁ of the distance. David runs at the same average speed throughout the race and Neave’s average speed is 48 m/min slower than David’s. If Neave wants to finish the race at the same time as David, 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 David ran more than Neave in first 20 min
= 20 x 48
= 960 m

Fraction of the entire distance that was covered by David more than Neave in the first 20 min
= ⁵₁₁ - ³₁₁
= ²₁₁

²₁₁ of the entire distance = 960 m
¹₁₁ of the entire distance = 960 ÷ 2 = 480 m

Distance that Neave ran in the first 20 min
= 3 x 480
= 1440 m

Neave's average speed
= 1440 ÷ 20
= 72 m/min

David's average speed
= 72 + 48
= 120 m/min

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

¹₁₁ of the entire distance = 480 m
⁶₁₁ of the entire distance = 6 x 480 = 2880 m

Duration that David would take to complete
= 2880 ÷ 120
= 24 min

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

⁸₁₁ of the entire distance = 8 x 480 = 3840 m  

Speed that Neave needs to take to complete distance at the same time as David
= 3840 ÷ 24
= 160 m/min

Increase in Neave's average speed
= 160 - 72
= 88 m/min

Percentage increase in Neave's average speed
= ⁸⁸₇₂ x 100%
≈ 122%

Answer(s): 122%