After 20 minutes into a race, Elijah has run ⁵₁₁ of the route while Bryan has covered only ³₁₁ of the distance. Elijah runs at the same average speed throughout the race and Bryan’s average speed is 102 m/min slower than Elijah’s. If Bryan wants to finish the race at the same time as Elijah, 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 Elijah ran more than Bryan in first 20 min
= 20 x 102
= 2040 m

Fraction of the entire distance that was covered by Elijah more than Bryan in the first 20 min
= ⁵₁₁ - ³₁₁
= ²₁₁

²₁₁ of the entire distance = 2040 m
¹₁₁ of the entire distance = 2040 ÷ 2 = 1020 m

Distance that Bryan ran in the first 20 min
= 3 x 1020
= 3060 m

Bryan's average speed
= 3060 ÷ 20
= 153 m/min

Elijah's average speed
= 153 + 102
= 255 m/min

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

¹₁₁ of the entire distance = 1020 m
⁶₁₁ of the entire distance = 6 x 1020 = 6120 m

Duration that Elijah would take to complete
= 6120 ÷ 255
= 24 min

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

⁸₁₁ of the entire distance = 8 x 1020 = 8160 m  

Speed that Bryan needs to take to complete distance at the same time as Elijah
= 8160 ÷ 24
= 340 m/min

Increase in Bryan's average speed
= 340 - 153
= 187 m/min

Percentage increase in Bryan's average speed
= ¹⁸⁷₁₅₃ x 100%
≈ 122%

Answer(s): 122%