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

Fraction of the entire distance that was covered by Zeph more than Bryan 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 Bryan ran in the first 35 min
= 4 x 1120
= 4480 m

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

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

Fraction of the journey that Zeph 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 Zeph would take to complete
= 6720 ÷ 224
= 30 min

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

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

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

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

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

Answer(s): 163%