After 35 minutes into a race, Sean has run ⁷₁₃ of the route while Dylan has covered only ⁴₁₃ of the distance. Sean runs at the same average speed throughout the race and Dylan’s average speed is 54 m/min slower than Sean’s. If Dylan wants to finish the race at the same time as Sean, 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 Sean ran more than Dylan in first 35 min
= 35 x 54
= 1890 m

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

³₁₃ of the entire distance = 1890 m
¹₁₃ of the entire distance = 1890 ÷ 3 = 630 m

Distance that Dylan ran in the first 35 min
= 4 x 630
= 2520 m

Dylan's average speed
= 2520 ÷ 35
= 72 m/min

Sean's average speed
= 72 + 54
= 126 m/min

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

¹₁₃ of the entire distance = 630 m
⁶₁₃ of the entire distance = 6 x 630 = 3780 m

Duration that Sean would take to complete
= 3780 ÷ 126
= 30 min

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

⁹₁₃ of the entire distance = 9 x 630 = 5670 m  

Speed that Dylan needs to take to complete distance at the same time as Sean
= 5670 ÷ 30
= 189 m/min

Increase in Dylan's average speed
= 189 - 72
= 117 m/min

Percentage increase in Dylan's average speed
= ¹¹⁷₇₂ x 100%
≈ 163%

Answer(s): 163%