After 30 minutes into a race, Dylan has run ⁶₁₃ of the route while David has covered only ⁴₁₃ of the distance. Dylan runs at the same average speed throughout the race and David’s average speed is 63 m/min slower than Dylan’s. If David wants to finish the race at the same time as Dylan, 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 Dylan ran more than David in first 30 min
= 30 x 63
= 1890 m

Fraction of the entire distance that was covered by Dylan more than David in the first 30 min
= ⁶₁₃ - ⁴₁₃
= ²₁₃

²₁₃ of the entire distance = 1890 m
¹₁₃ of the entire distance = 1890 ÷ 2 = 945 m

Distance that David ran in the first 30 min
= 4 x 945
= 3780 m

David's average speed
= 3780 ÷ 30
= 126 m/min

Dylan's average speed
= 126 + 63
= 189 m/min

Fraction of the journey that Dylan needed to run to complete the race
= 1 - ⁶₁₃
= ⁷₁₃

¹₁₃ of the entire distance = 945 m
⁷₁₃ of the entire distance = 7 x 945 = 6615 m

Duration that Dylan would take to complete
= 6615 ÷ 189
= 35 min

Fraction of the journey that Dylan needed to run to complete the race
= 1 - ⁴₁₃
= ⁹₁₃

⁹₁₃ of the entire distance = 9 x 945 = 8505 m  

Speed that David needs to take to complete distance at the same time as Dylan
= 8505 ÷ 35
= 243 m/min

Increase in David's average speed
= 243 - 126
= 117 m/min

Percentage increase in David's average speed
= ¹¹⁷₁₂₆ x 100%
≈ 93%

Answer(s): 93%