After 35 minutes into a race, Bryan has run ⁷₁₃ of the route while Charlie has covered only ⁴₁₃ of the distance. Bryan runs at the same average speed throughout the race and Charlie’s average speed is 96 m/min slower than Bryan’s. If Charlie wants to finish the race at the same time as Bryan, 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 Bryan ran more than Charlie in first 35 min
= 35 x 96
= 3360 m

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

³₁₃ of the entire distance = 3360 m
¹₁₃ of the entire distance = 3360 ÷ 3 = 1120 m

Distance that Charlie ran in the first 35 min
= 4 x 1120
= 4480 m

Charlie's average speed
= 4480 ÷ 35
= 128 m/min

Bryan's average speed
= 128 + 96
= 224 m/min

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

¹₁₃ of the entire distance = 1120 m
⁶₁₃ of the entire distance = 6 x 1120 = 6720 m

Duration that Bryan would take to complete
= 6720 ÷ 224
= 30 min

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

⁹₁₃ of the entire distance = 9 x 1120 = 10080 m  

Speed that Charlie needs to take to complete distance at the same time as Bryan
= 10080 ÷ 30
= 336 m/min

Increase in Charlie's average speed
= 336 - 128
= 208 m/min

Percentage increase in Charlie's average speed
= ²⁰⁸₁₂₈ x 100%
≈ 163%

Answer(s): 163%