After 35 minutes into a race, Peter has run ⁷₁₃ of the route while Jack has covered only ⁴₁₃ of the distance. Peter runs at the same average speed throughout the race and Jack’s average speed is 90 m/min slower than Peter’s. If Jack wants to finish the race at the same time as Peter, 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 Peter ran more than Jack in first 35 min
= 35 x 90
= 3150 m

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

³₁₃ of the entire distance = 3150 m
¹₁₃ of the entire distance = 3150 ÷ 3 = 1050 m

Distance that Jack ran in the first 35 min
= 4 x 1050
= 4200 m

Jack's average speed
= 4200 ÷ 35
= 120 m/min

Peter's average speed
= 120 + 90
= 210 m/min

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

¹₁₃ of the entire distance = 1050 m
⁶₁₃ of the entire distance = 6 x 1050 = 6300 m

Duration that Peter would take to complete
= 6300 ÷ 210
= 30 min

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

⁹₁₃ of the entire distance = 9 x 1050 = 9450 m  

Speed that Jack needs to take to complete distance at the same time as Peter
= 9450 ÷ 30
= 315 m/min

Increase in Jack's average speed
= 315 - 120
= 195 m/min

Percentage increase in Jack's average speed
= ¹⁹⁵₁₂₀ x 100%
≈ 163%

Answer(s): 163%