After 30 minutes into a race, Simon has run ⁶₁₃ of the route while Bryan has covered only ⁴₁₃ of the distance. Simon runs at the same average speed throughout the race and Bryan’s average speed is 77 m/min slower than Simon’s. If Bryan wants to finish the race at the same time as Simon, 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 Simon ran more than Bryan in first 30 min
= 30 x 77
= 2310 m

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

²₁₃ of the entire distance = 2310 m
¹₁₃ of the entire distance = 2310 ÷ 2 = 1155 m

Distance that Bryan ran in the first 30 min
= 4 x 1155
= 4620 m

Bryan's average speed
= 4620 ÷ 30
= 154 m/min

Simon's average speed
= 154 + 77
= 231 m/min

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

¹₁₃ of the entire distance = 1155 m
⁷₁₃ of the entire distance = 7 x 1155 = 8085 m

Duration that Simon would take to complete
= 8085 ÷ 231
= 35 min

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

⁹₁₃ of the entire distance = 9 x 1155 = 10395 m  

Speed that Bryan needs to take to complete distance at the same time as Simon
= 10395 ÷ 35
= 297 m/min

Increase in Bryan's average speed
= 297 - 154
= 143 m/min

Percentage increase in Bryan's average speed
= ¹⁴³₁₅₄ x 100%
≈ 93%

Answer(s): 93%