After 35 minutes into a race, Michael has run ⁷₁₃ of the route while Riordan has covered only ⁴₁₃ of the distance. Michael runs at the same average speed throughout the race and Riordan’s average speed is 102 m/min slower than Michael’s. If Riordan wants to finish the race at the same time as Michael, 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 Michael ran more than Riordan in first 35 min
= 35 x 102
= 3570 m

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

³₁₃ of the entire distance = 3570 m
¹₁₃ of the entire distance = 3570 ÷ 3 = 1190 m

Distance that Riordan ran in the first 35 min
= 4 x 1190
= 4760 m

Riordan's average speed
= 4760 ÷ 35
= 136 m/min

Michael's average speed
= 136 + 102
= 238 m/min

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

¹₁₃ of the entire distance = 1190 m
⁶₁₃ of the entire distance = 6 x 1190 = 7140 m

Duration that Michael would take to complete
= 7140 ÷ 238
= 30 min

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

⁹₁₃ of the entire distance = 9 x 1190 = 10710 m  

Speed that Riordan needs to take to complete distance at the same time as Michael
= 10710 ÷ 30
= 357 m/min

Increase in Riordan's average speed
= 357 - 136
= 221 m/min

Percentage increase in Riordan's average speed
= ²²¹₁₃₆ x 100%
≈ 163%

Answer(s): 163%