After 40 minutes into a race, Jack has run ⁸₁₁ of the route while Archie has covered only ²₁₁ of the distance. Jack runs at the same average speed throughout the race and Archie’s average speed is 105 m/min slower than Jack’s. If Archie wants to finish the race at the same time as Jack, 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 Jack ran more than Archie in first 40 min
= 40 x 105
= 4200 m

Fraction of the entire distance that was covered by Jack more than Archie in the first 40 min
= ⁸₁₁ - ²₁₁
= ⁶₁₁

⁶₁₁ of the entire distance = 4200 m
¹₁₁ of the entire distance = 4200 ÷ 6 = 700 m

Distance that Archie ran in the first 40 min
= 2 x 700
= 1400 m

Archie's average speed
= 1400 ÷ 40
= 35 m/min

Jack's average speed
= 35 + 105
= 140 m/min

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

¹₁₁ of the entire distance = 700 m
³₁₁ of the entire distance = 3 x 700 = 2100 m

Duration that Jack would take to complete
= 2100 ÷ 140
= 15 min

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

⁹₁₁ of the entire distance = 9 x 700 = 6300 m  

Speed that Archie needs to take to complete distance at the same time as Jack
= 6300 ÷ 15
= 420 m/min

Increase in Archie's average speed
= 420 - 35
= 385 m/min

Percentage increase in Archie's average speed
= ³⁸⁵₃₅ x 100%
≈ 1100%

Answer(s): 1100%