After 30 minutes into a race, Oliver has run ⁵₁₁ of the route while Paul has covered only ³₁₁ of the distance. Oliver runs at the same average speed throughout the race and Paul’s average speed is 108 m/min slower than Oliver’s. If Paul wants to finish the race at the same time as Oliver, 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 Oliver ran more than Paul in first 30 min
= 30 x 108
= 3240 m

Fraction of the entire distance that was covered by Oliver more than Paul in the first 30 min
= ⁵₁₁ - ³₁₁
= ²₁₁

²₁₁ of the entire distance = 3240 m
¹₁₁ of the entire distance = 3240 ÷ 2 = 1620 m

Distance that Paul ran in the first 30 min
= 3 x 1620
= 4860 m

Paul's average speed
= 4860 ÷ 30
= 162 m/min

Oliver's average speed
= 162 + 108
= 270 m/min

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

¹₁₁ of the entire distance = 1620 m
⁶₁₁ of the entire distance = 6 x 1620 = 9720 m

Duration that Oliver would take to complete
= 9720 ÷ 270
= 36 min

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

⁸₁₁ of the entire distance = 8 x 1620 = 12960 m  

Speed that Paul needs to take to complete distance at the same time as Oliver
= 12960 ÷ 36
= 360 m/min

Increase in Paul's average speed
= 360 - 162
= 198 m/min

Percentage increase in Paul's average speed
= ¹⁹⁸₁₆₂ x 100%
≈ 122%

Answer(s): 122%