After 30 minutes into a race, George has run ⁶₁₃ of the route while Ian has covered only ⁴₁₃ of the distance. George runs at the same average speed throughout the race and Ian’s average speed is 98 m/min slower than George’s. If Ian wants to finish the race at the same time as George, 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 George ran more than Ian in first 30 min
= 30 x 98
= 2940 m

Fraction of the entire distance that was covered by George more than Ian in the first 30 min
= ⁶₁₃ - ⁴₁₃
= ²₁₃

²₁₃ of the entire distance = 2940 m
¹₁₃ of the entire distance = 2940 ÷ 2 = 1470 m

Distance that Ian ran in the first 30 min
= 4 x 1470
= 5880 m

Ian's average speed
= 5880 ÷ 30
= 196 m/min

George's average speed
= 196 + 98
= 294 m/min

Fraction of the journey that George needed to run to complete the race
= 1 - ⁶₁₃
= ⁷₁₃

¹₁₃ of the entire distance = 1470 m
⁷₁₃ of the entire distance = 7 x 1470 = 10290 m

Duration that George would take to complete
= 10290 ÷ 294
= 35 min

Fraction of the journey that George needed to run to complete the race
= 1 - ⁴₁₃
= ⁹₁₃

⁹₁₃ of the entire distance = 9 x 1470 = 13230 m  

Speed that Ian needs to take to complete distance at the same time as George
= 13230 ÷ 35
= 378 m/min

Increase in Ian's average speed
= 378 - 196
= 182 m/min

Percentage increase in Ian's average speed
= ¹⁸²₁₉₆ x 100%
≈ 93%

Answer(s): 93%