After 15 minutes into a race, Vincent has run ⁵₁₁ of the route while Jack has covered only ²₁₁ of the distance. Vincent runs at the same average speed throughout the race and Jack’s average speed is 78 m/min slower than Vincent’s. If Jack wants to finish the race at the same time as Vincent, 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 Vincent ran more than Jack in first 15 min
= 15 x 78
= 1170 m

Fraction of the entire distance that was covered by Vincent more than Jack in the first 15 min
= ⁵₁₁ - ²₁₁
= ³₁₁

³₁₁ of the entire distance = 1170 m
¹₁₁ of the entire distance = 1170 ÷ 3 = 390 m

Distance that Jack ran in the first 15 min
= 2 x 390
= 780 m

Jack's average speed
= 780 ÷ 15
= 52 m/min

Vincent's average speed
= 52 + 78
= 130 m/min

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

¹₁₁ of the entire distance = 390 m
⁶₁₁ of the entire distance = 6 x 390 = 2340 m

Duration that Vincent would take to complete
= 2340 ÷ 130
= 18 min

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

⁹₁₁ of the entire distance = 9 x 390 = 3510 m  

Speed that Jack needs to take to complete distance at the same time as Vincent
= 3510 ÷ 18
= 195 m/min

Increase in Jack's average speed
= 195 - 52
= 143 m/min

Percentage increase in Jack's average speed
= ¹⁴³₅₂ x 100%
≈ 275%

Answer(s): 275%