After 35 minutes into a race, Liam has run ⁵₁₁ of the route while Henry has covered only ²₁₁ of the distance. Liam runs at the same average speed throughout the race and Henry’s average speed is 66 m/min slower than Liam’s. If Henry wants to finish the race at the same time as Liam, 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 Liam ran more than Henry in first 35 min
= 35 x 66
= 2310 m

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

³₁₁ of the entire distance = 2310 m
¹₁₁ of the entire distance = 2310 ÷ 3 = 770 m

Distance that Henry ran in the first 35 min
= 2 x 770
= 1540 m

Henry's average speed
= 1540 ÷ 35
= 44 m/min

Liam's average speed
= 44 + 66
= 110 m/min

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

¹₁₁ of the entire distance = 770 m
⁶₁₁ of the entire distance = 6 x 770 = 4620 m

Duration that Liam would take to complete
= 4620 ÷ 110
= 42 min

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

⁹₁₁ of the entire distance = 9 x 770 = 6930 m  

Speed that Henry needs to take to complete distance at the same time as Liam
= 6930 ÷ 42
= 165 m/min

Increase in Henry's average speed
= 165 - 44
= 121 m/min

Percentage increase in Henry's average speed
= ¹²¹₄₄ x 100%
≈ 275%

Answer(s): 275%