After 25 minutes into a race, Tom has run ⁵₁₁ of the route while Ian has covered only ²₁₁ of the distance. Tom runs at the same average speed throughout the race and Ian’s average speed is 72 m/min slower than Tom’s. If Ian wants to finish the race at the same time as Tom, 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 Tom ran more than Ian in first 25 min
= 25 x 72
= 1800 m

Fraction of the entire distance that was covered by Tom more than Ian in the first 25 min
= ⁵₁₁ - ²₁₁
= ³₁₁

³₁₁ of the entire distance = 1800 m
¹₁₁ of the entire distance = 1800 ÷ 3 = 600 m

Distance that Ian ran in the first 25 min
= 2 x 600
= 1200 m

Ian's average speed
= 1200 ÷ 25
= 48 m/min

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

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

¹₁₁ of the entire distance = 600 m
⁶₁₁ of the entire distance = 6 x 600 = 3600 m

Duration that Tom would take to complete
= 3600 ÷ 120
= 30 min

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

⁹₁₁ of the entire distance = 9 x 600 = 5400 m  

Speed that Ian needs to take to complete distance at the same time as Tom
= 5400 ÷ 30
= 180 m/min

Increase in Ian's average speed
= 180 - 48
= 132 m/min

Percentage increase in Ian's average speed
= ¹³²₄₈ x 100%
≈ 275%

Answer(s): 275%