After 40 minutes into a race, Mark has run ⁵₁₁ of the route while Warren has covered only ³₁₁ of the distance. Mark runs at the same average speed throughout the race and Warren’s average speed is 102 m/min slower than Mark’s. If Warren wants to finish the race at the same time as Mark, 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 Mark ran more than Warren in first 40 min
= 40 x 102
= 4080 m

Fraction of the entire distance that was covered by Mark more than Warren in the first 40 min
= ⁵₁₁ - ³₁₁
= ²₁₁

²₁₁ of the entire distance = 4080 m
¹₁₁ of the entire distance = 4080 ÷ 2 = 2040 m

Distance that Warren ran in the first 40 min
= 3 x 2040
= 6120 m

Warren's average speed
= 6120 ÷ 40
= 153 m/min

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

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

¹₁₁ of the entire distance = 2040 m
⁶₁₁ of the entire distance = 6 x 2040 = 12240 m

Duration that Mark would take to complete
= 12240 ÷ 255
= 48 min

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

⁸₁₁ of the entire distance = 8 x 2040 = 16320 m  

Speed that Warren needs to take to complete distance at the same time as Mark
= 16320 ÷ 48
= 340 m/min

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

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

Answer(s): 122%