After 30 minutes into a race, Ahmad has run ⁶₁₃ of the route while Charlie has covered only ⁴₁₃ of the distance. Ahmad runs at the same average speed throughout the race and Charlie’s average speed is 91 m/min slower than Ahmad’s. If Charlie wants to finish the race at the same time as Ahmad, 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 Ahmad ran more than Charlie in first 30 min
= 30 x 91
= 2730 m

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

²₁₃ of the entire distance = 2730 m
¹₁₃ of the entire distance = 2730 ÷ 2 = 1365 m

Distance that Charlie ran in the first 30 min
= 4 x 1365
= 5460 m

Charlie's average speed
= 5460 ÷ 30
= 182 m/min

Ahmad's average speed
= 182 + 91
= 273 m/min

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

¹₁₃ of the entire distance = 1365 m
⁷₁₃ of the entire distance = 7 x 1365 = 9555 m

Duration that Ahmad would take to complete
= 9555 ÷ 273
= 35 min

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

⁹₁₃ of the entire distance = 9 x 1365 = 12285 m  

Speed that Charlie needs to take to complete distance at the same time as Ahmad
= 12285 ÷ 35
= 351 m/min

Increase in Charlie's average speed
= 351 - 182
= 169 m/min

Percentage increase in Charlie's average speed
= ¹⁶⁹₁₈₂ x 100%
≈ 93%

Answer(s): 93%