After 40 minutes into a race, Ahmad has run ⁵₁₁ of the route while Warren has covered only ²₁₁ of the distance. Ahmad runs at the same average speed throughout the race and Warren’s average speed is 30 m/min slower than Ahmad’s. If Warren wants to finish the race at the same time as Ahmad, 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 Ahmad ran more than Warren in first 40 min
= 40 x 30
= 1200 m

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

³₁₁ of the entire distance = 1200 m
¹₁₁ of the entire distance = 1200 ÷ 3 = 400 m

Distance that Warren ran in the first 40 min
= 2 x 400
= 800 m

Warren's average speed
= 800 ÷ 40
= 20 m/min

Ahmad's average speed
= 20 + 30
= 50 m/min

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

¹₁₁ of the entire distance = 400 m
⁶₁₁ of the entire distance = 6 x 400 = 2400 m

Duration that Ahmad would take to complete
= 2400 ÷ 50
= 48 min

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

⁹₁₁ of the entire distance = 9 x 400 = 3600 m  

Speed that Warren needs to take to complete distance at the same time as Ahmad
= 3600 ÷ 48
= 75 m/min

Increase in Warren's average speed
= 75 - 20
= 55 m/min

Percentage increase in Warren's average speed
= ⁵⁵₂₀ x 100%
≈ 275%

Answer(s): 275%