After 15 minutes into a race, Dylan has run ⁵₁₁ of the route while Howard has covered only ²₁₁ of the distance. Dylan runs at the same average speed throughout the race and Howard’s average speed is 66 m/min slower than Dylan’s. If Howard wants to finish the race at the same time as Dylan, 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 Dylan ran more than Howard in first 15 min
= 15 x 66
= 990 m

Fraction of the entire distance that was covered by Dylan more than Howard in the first 15 min
= ⁵₁₁ - ²₁₁
= ³₁₁

³₁₁ of the entire distance = 990 m
¹₁₁ of the entire distance = 990 ÷ 3 = 330 m

Distance that Howard ran in the first 15 min
= 2 x 330
= 660 m

Howard's average speed
= 660 ÷ 15
= 44 m/min

Dylan's average speed
= 44 + 66
= 110 m/min

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

¹₁₁ of the entire distance = 330 m
⁶₁₁ of the entire distance = 6 x 330 = 1980 m

Duration that Dylan would take to complete
= 1980 ÷ 110
= 18 min

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

⁹₁₁ of the entire distance = 9 x 330 = 2970 m  

Speed that Howard needs to take to complete distance at the same time as Dylan
= 2970 ÷ 18
= 165 m/min

Increase in Howard's average speed
= 165 - 44
= 121 m/min

Percentage increase in Howard's average speed
= ¹²¹₄₄ x 100%
≈ 275%

Answer(s): 275%