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

Fraction of the entire distance that was covered by Harry more than Pierre 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 Pierre ran in the first 30 min
= 4 x 945
= 3780 m

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

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

Fraction of the journey that Harry 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 Harry would take to complete
= 6615 ÷ 189
= 35 min

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

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

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

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

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

Answer(s): 93%