After 15 minutes into a race, Jenson has run ⁵₁₁ of the route while Elijah has covered only ³₁₁ of the distance. Jenson runs at the same average speed throughout the race and Elijah’s average speed is 120 m/min slower than Jenson’s. If Elijah 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 Elijah in first 15 min
= 15 x 120
= 1800 m

Fraction of the entire distance that was covered by Jenson more than Elijah in the first 15 min
= ⁵₁₁ - ³₁₁
= ²₁₁

²₁₁ of the entire distance = 1800 m
¹₁₁ of the entire distance = 1800 ÷ 2 = 900 m

Distance that Elijah ran in the first 15 min
= 3 x 900
= 2700 m

Elijah's average speed
= 2700 ÷ 15
= 180 m/min

Jenson's average speed
= 180 + 120
= 300 m/min

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

¹₁₁ of the entire distance = 900 m
⁶₁₁ of the entire distance = 6 x 900 = 5400 m

Duration that Jenson would take to complete
= 5400 ÷ 300
= 18 min

Fraction of the journey that Jenson needed to run to complete the race
= 1 - ³₁₁
= ⁸₁₁

⁸₁₁ of the entire distance = 8 x 900 = 7200 m  

Speed that Elijah needs to take to complete distance at the same time as Jenson
= 7200 ÷ 18
= 400 m/min

Increase in Elijah's average speed
= 400 - 180
= 220 m/min

Percentage increase in Elijah's average speed
= ²²⁰₁₈₀ x 100%
≈ 122%

Answer(s): 122%