After 25 minutes into a race, Tom has run ⁵₁₁ of the route while Jack has covered only ³₁₁ of the distance. Tom runs at the same average speed throughout the race and Jack’s average speed is 60 m/min slower than Tom’s. If Jack wants to finish the race at the same time as Tom, 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 Tom ran more than Jack in first 25 min
= 25 x 60
= 1500 m

Fraction of the entire distance that was covered by Tom more than Jack in the first 25 min
= ⁵₁₁ - ³₁₁
= ²₁₁

²₁₁ of the entire distance = 1500 m
¹₁₁ of the entire distance = 1500 ÷ 2 = 750 m

Distance that Jack ran in the first 25 min
= 3 x 750
= 2250 m

Jack's average speed
= 2250 ÷ 25
= 90 m/min

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

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

¹₁₁ of the entire distance = 750 m
⁶₁₁ of the entire distance = 6 x 750 = 4500 m

Duration that Tom would take to complete
= 4500 ÷ 150
= 30 min

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

⁸₁₁ of the entire distance = 8 x 750 = 6000 m  

Speed that Jack needs to take to complete distance at the same time as Tom
= 6000 ÷ 30
= 200 m/min

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

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

Answer(s): 122%