After 35 minutes into a race, Justin has run ⁵₁₁ of the route while Tom has covered only ²₁₁ of the distance. Justin runs at the same average speed throughout the race and Tom’s average speed is 54 m/min slower than Justin’s. If Tom wants to finish the race at the same time as Justin, 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 Justin ran more than Tom in first 35 min
= 35 x 54
= 1890 m

Fraction of the entire distance that was covered by Justin more than Tom in the first 35 min
= ⁵₁₁ - ²₁₁
= ³₁₁

³₁₁ of the entire distance = 1890 m
¹₁₁ of the entire distance = 1890 ÷ 3 = 630 m

Distance that Tom ran in the first 35 min
= 2 x 630
= 1260 m

Tom's average speed
= 1260 ÷ 35
= 36 m/min

Justin's average speed
= 36 + 54
= 90 m/min

Fraction of the journey that Justin needed to run to complete the race
= 1 - ⁵₁₁
= ⁶₁₁

¹₁₁ of the entire distance = 630 m
⁶₁₁ of the entire distance = 6 x 630 = 3780 m

Duration that Justin would take to complete
= 3780 ÷ 90
= 42 min

Fraction of the journey that Justin needed to run to complete the race
= 1 - ²₁₁
= ⁹₁₁

⁹₁₁ of the entire distance = 9 x 630 = 5670 m  

Speed that Tom needs to take to complete distance at the same time as Justin
= 5670 ÷ 42
= 135 m/min

Increase in Tom's average speed
= 135 - 36
= 99 m/min

Percentage increase in Tom's average speed
= ⁹⁹₃₆ x 100%
≈ 275%

Answer(s): 275%