After 35 minutes into a race, George has run ⁷₁₃ of the route while Warren has covered only ⁴₁₃ of the distance. George runs at the same average speed throughout the race and Warren’s average speed is 78 m/min slower than George’s. If Warren 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 Warren in first 35 min
= 35 x 78
= 2730 m

Fraction of the entire distance that was covered by George more than Warren in the first 35 min
= ⁷₁₃ - ⁴₁₃
= ³₁₃

³₁₃ of the entire distance = 2730 m
¹₁₃ of the entire distance = 2730 ÷ 3 = 910 m

Distance that Warren ran in the first 35 min
= 4 x 910
= 3640 m

Warren's average speed
= 3640 ÷ 35
= 104 m/min

George's average speed
= 104 + 78
= 182 m/min

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

¹₁₃ of the entire distance = 910 m
⁶₁₃ of the entire distance = 6 x 910 = 5460 m

Duration that George would take to complete
= 5460 ÷ 182
= 30 min

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

⁹₁₃ of the entire distance = 9 x 910 = 8190 m  

Speed that Warren needs to take to complete distance at the same time as George
= 8190 ÷ 30
= 273 m/min

Increase in Warren's average speed
= 273 - 104
= 169 m/min

Percentage increase in Warren's average speed
= ¹⁶⁹₁₀₄ x 100%
≈ 163%

Answer(s): 163%