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

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

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

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

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

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

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

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

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

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

Answer(s): 163%