After 35 minutes into a race, Asher has run ⁷₁₃ of the route while Luis has covered only ⁴₁₃ of the distance. Asher runs at the same average speed throughout the race and Luis’s average speed is 48 m/min slower than Asher’s. If Luis wants to finish the race at the same time as Asher, 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 Asher ran more than Luis in first 35 min
= 35 x 48
= 1680 m

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

³₁₃ of the entire distance = 1680 m
¹₁₃ of the entire distance = 1680 ÷ 3 = 560 m

Distance that Luis ran in the first 35 min
= 4 x 560
= 2240 m

Luis's average speed
= 2240 ÷ 35
= 64 m/min

Asher's average speed
= 64 + 48
= 112 m/min

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

¹₁₃ of the entire distance = 560 m
⁶₁₃ of the entire distance = 6 x 560 = 3360 m

Duration that Asher would take to complete
= 3360 ÷ 112
= 30 min

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

⁹₁₃ of the entire distance = 9 x 560 = 5040 m  

Speed that Luis needs to take to complete distance at the same time as Asher
= 5040 ÷ 30
= 168 m/min

Increase in Luis's average speed
= 168 - 64
= 104 m/min

Percentage increase in Luis's average speed
= ¹⁰⁴₆₄ x 100%
≈ 163%

Answer(s): 163%