After 25 minutes into a race, Daniel has run ⁵₁₁ of the route while Tom has covered only ³₁₁ of the distance. Daniel runs at the same average speed throughout the race and Tom’s average speed is 102 m/min slower than Daniel’s. If Tom wants to finish the race at the same time as Daniel, 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 Daniel ran more than Tom in first 25 min
= 25 x 102
= 2550 m

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

²₁₁ of the entire distance = 2550 m
¹₁₁ of the entire distance = 2550 ÷ 2 = 1275 m

Distance that Tom ran in the first 25 min
= 3 x 1275
= 3825 m

Tom's average speed
= 3825 ÷ 25
= 153 m/min

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

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

¹₁₁ of the entire distance = 1275 m
⁶₁₁ of the entire distance = 6 x 1275 = 7650 m

Duration that Daniel would take to complete
= 7650 ÷ 255
= 30 min

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

⁸₁₁ of the entire distance = 8 x 1275 = 10200 m  

Speed that Tom needs to take to complete distance at the same time as Daniel
= 10200 ÷ 30
= 340 m/min

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

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

Answer(s): 122%