After 40 minutes into a race, David has run ⁵₁₁ of the route while Ian has covered only ²₁₁ of the distance. David runs at the same average speed throughout the race and Ian’s average speed is 78 m/min slower than David’s. If Ian 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 Ian in first 40 min
= 40 x 78
= 3120 m

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

³₁₁ of the entire distance = 3120 m
¹₁₁ of the entire distance = 3120 ÷ 3 = 1040 m

Distance that Ian ran in the first 40 min
= 2 x 1040
= 2080 m

Ian's average speed
= 2080 ÷ 40
= 52 m/min

David's average speed
= 52 + 78
= 130 m/min

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

¹₁₁ of the entire distance = 1040 m
⁶₁₁ of the entire distance = 6 x 1040 = 6240 m

Duration that David would take to complete
= 6240 ÷ 130
= 48 min

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

⁹₁₁ of the entire distance = 9 x 1040 = 9360 m  

Speed that Ian needs to take to complete distance at the same time as David
= 9360 ÷ 48
= 195 m/min

Increase in Ian's average speed
= 195 - 52
= 143 m/min

Percentage increase in Ian's average speed
= ¹⁴³₅₂ x 100%
≈ 275%

Answer(s): 275%