After 35 minutes into a race, Xavier has run ⁷₁₃ of the route while Peter has covered only ⁴₁₃ of the distance. Xavier runs at the same average speed throughout the race and Peter’s average speed is 42 m/min slower than Xavier’s. If Peter wants to finish the race at the same time as Xavier, 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 Xavier ran more than Peter in first 35 min
= 35 x 42
= 1470 m

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

³₁₃ of the entire distance = 1470 m
¹₁₃ of the entire distance = 1470 ÷ 3 = 490 m

Distance that Peter ran in the first 35 min
= 4 x 490
= 1960 m

Peter's average speed
= 1960 ÷ 35
= 56 m/min

Xavier's average speed
= 56 + 42
= 98 m/min

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

¹₁₃ of the entire distance = 490 m
⁶₁₃ of the entire distance = 6 x 490 = 2940 m

Duration that Xavier would take to complete
= 2940 ÷ 98
= 30 min

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

⁹₁₃ of the entire distance = 9 x 490 = 4410 m  

Speed that Peter needs to take to complete distance at the same time as Xavier
= 4410 ÷ 30
= 147 m/min

Increase in Peter's average speed
= 147 - 56
= 91 m/min

Percentage increase in Peter's average speed
= ⁹¹₅₆ x 100%
≈ 163%

Answer(s): 163%