After 20 minutes into a race, Glen has run ⁵₁₁ of the route while Paul has covered only ³₁₁ of the distance. Glen runs at the same average speed throughout the race and Paul’s average speed is 60 m/min slower than Glen’s. If Paul wants to finish the race at the same time as Glen, 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 Glen ran more than Paul in first 20 min
= 20 x 60
= 1200 m

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

²₁₁ of the entire distance = 1200 m
¹₁₁ of the entire distance = 1200 ÷ 2 = 600 m

Distance that Paul ran in the first 20 min
= 3 x 600
= 1800 m

Paul's average speed
= 1800 ÷ 20
= 90 m/min

Glen's average speed
= 90 + 60
= 150 m/min

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

¹₁₁ of the entire distance = 600 m
⁶₁₁ of the entire distance = 6 x 600 = 3600 m

Duration that Glen would take to complete
= 3600 ÷ 150
= 24 min

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

⁸₁₁ of the entire distance = 8 x 600 = 4800 m  

Speed that Paul needs to take to complete distance at the same time as Glen
= 4800 ÷ 24
= 200 m/min

Increase in Paul's average speed
= 200 - 90
= 110 m/min

Percentage increase in Paul's average speed
= ¹¹⁰₉₀ x 100%
≈ 122%

Answer(s): 122%