After 40 minutes into a race, Charlie has run ⁵₁₁ of the route while Tom has covered only ³₁₁ of the distance. Charlie runs at the same average speed throughout the race and Tom’s average speed is 48 m/min slower than Charlie’s. If Tom wants to finish the race at the same time as Charlie, 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 Charlie ran more than Tom in first 40 min
= 40 x 48
= 1920 m

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

²₁₁ of the entire distance = 1920 m
¹₁₁ of the entire distance = 1920 ÷ 2 = 960 m

Distance that Tom ran in the first 40 min
= 3 x 960
= 2880 m

Tom's average speed
= 2880 ÷ 40
= 72 m/min

Charlie's average speed
= 72 + 48
= 120 m/min

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

¹₁₁ of the entire distance = 960 m
⁶₁₁ of the entire distance = 6 x 960 = 5760 m

Duration that Charlie would take to complete
= 5760 ÷ 120
= 48 min

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

⁸₁₁ of the entire distance = 8 x 960 = 7680 m  

Speed that Tom needs to take to complete distance at the same time as Charlie
= 7680 ÷ 48
= 160 m/min

Increase in Tom's average speed
= 160 - 72
= 88 m/min

Percentage increase in Tom's average speed
= ⁸⁸₇₂ x 100%
≈ 122%

Answer(s): 122%