After 40 minutes into a race, Tim has run ⁵₁₁ of the route while Henry has covered only ²₁₁ of the distance. Tim runs at the same average speed throughout the race and Henry’s average speed is 54 m/min slower than Tim’s. If Henry wants to finish the race at the same time as Tim, 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 Tim ran more than Henry in first 40 min
= 40 x 54
= 2160 m

Fraction of the entire distance that was covered by Tim more than Henry in the first 40 min
= ⁵₁₁ - ²₁₁
= ³₁₁

³₁₁ of the entire distance = 2160 m
¹₁₁ of the entire distance = 2160 ÷ 3 = 720 m

Distance that Henry ran in the first 40 min
= 2 x 720
= 1440 m

Henry's average speed
= 1440 ÷ 40
= 36 m/min

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

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

¹₁₁ of the entire distance = 720 m
⁶₁₁ of the entire distance = 6 x 720 = 4320 m

Duration that Tim would take to complete
= 4320 ÷ 90
= 48 min

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

⁹₁₁ of the entire distance = 9 x 720 = 6480 m  

Speed that Henry needs to take to complete distance at the same time as Tim
= 6480 ÷ 48
= 135 m/min

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

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

Answer(s): 275%