After 35 minutes into a race, Reggie has run ⁷₁₃ of the route while Will has covered only ⁴₁₃ of the distance. Reggie runs at the same average speed throughout the race and Will’s average speed is 66 m/min slower than Reggie’s. If Will wants to finish the race at the same time as Reggie, 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 Reggie ran more than Will in first 35 min
= 35 x 66
= 2310 m

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

³₁₃ of the entire distance = 2310 m
¹₁₃ of the entire distance = 2310 ÷ 3 = 770 m

Distance that Will ran in the first 35 min
= 4 x 770
= 3080 m

Will's average speed
= 3080 ÷ 35
= 88 m/min

Reggie's average speed
= 88 + 66
= 154 m/min

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

¹₁₃ of the entire distance = 770 m
⁶₁₃ of the entire distance = 6 x 770 = 4620 m

Duration that Reggie would take to complete
= 4620 ÷ 154
= 30 min

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

⁹₁₃ of the entire distance = 9 x 770 = 6930 m  

Speed that Will needs to take to complete distance at the same time as Reggie
= 6930 ÷ 30
= 231 m/min

Increase in Will's average speed
= 231 - 88
= 143 m/min

Percentage increase in Will's average speed
= ¹⁴³₈₈ x 100%
≈ 163%

Answer(s): 163%