After 25 minutes into a race, Jenson has run ⁵₁₁ of the route while Ryan has covered only ²₁₁ of the distance. Jenson runs at the same average speed throughout the race and Ryan’s average speed is 78 m/min slower than Jenson’s. If Ryan wants to finish the race at the same time as Jenson, 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 Jenson ran more than Ryan in first 25 min
= 25 x 78
= 1950 m

Fraction of the entire distance that was covered by Jenson more than Ryan in the first 25 min
= ⁵₁₁ - ²₁₁
= ³₁₁

³₁₁ of the entire distance = 1950 m
¹₁₁ of the entire distance = 1950 ÷ 3 = 650 m

Distance that Ryan ran in the first 25 min
= 2 x 650
= 1300 m

Ryan's average speed
= 1300 ÷ 25
= 52 m/min

Jenson's average speed
= 52 + 78
= 130 m/min

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

¹₁₁ of the entire distance = 650 m
⁶₁₁ of the entire distance = 6 x 650 = 3900 m

Duration that Jenson would take to complete
= 3900 ÷ 130
= 30 min

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

⁹₁₁ of the entire distance = 9 x 650 = 5850 m  

Speed that Ryan needs to take to complete distance at the same time as Jenson
= 5850 ÷ 30
= 195 m/min

Increase in Ryan's average speed
= 195 - 52
= 143 m/min

Percentage increase in Ryan's average speed
= ¹⁴³₅₂ x 100%
≈ 275%

Answer(s): 275%