After 40 minutes into a race, Ben has run ⁵₁₁ of the route while Charlie has covered only ²₁₁ of the distance. Ben runs at the same average speed throughout the race and Charlie’s average speed is 48 m/min slower than Ben’s. If Charlie wants to finish the race at the same time as Ben, 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 Ben ran more than Charlie in first 40 min
= 40 x 48
= 1920 m

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

³₁₁ of the entire distance = 1920 m
¹₁₁ of the entire distance = 1920 ÷ 3 = 640 m

Distance that Charlie ran in the first 40 min
= 2 x 640
= 1280 m

Charlie's average speed
= 1280 ÷ 40
= 32 m/min

Ben's average speed
= 32 + 48
= 80 m/min

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

¹₁₁ of the entire distance = 640 m
⁶₁₁ of the entire distance = 6 x 640 = 3840 m

Duration that Ben would take to complete
= 3840 ÷ 80
= 48 min

Fraction of the journey that Ben needed to run to complete the race
= 1 - ²₁₁
= ⁹₁₁

⁹₁₁ of the entire distance = 9 x 640 = 5760 m  

Speed that Charlie needs to take to complete distance at the same time as Ben
= 5760 ÷ 48
= 120 m/min

Increase in Charlie's average speed
= 120 - 32
= 88 m/min

Percentage increase in Charlie's average speed
= ⁸⁸₃₂ x 100%
≈ 275%

Answer(s): 275%