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

Fraction of the entire distance that was covered by Nick more than Zeph 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 Zeph ran in the first 30 min
= 4 x 1155
= 4620 m

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

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

Fraction of the journey that Nick 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 Nick would take to complete
= 8085 ÷ 231
= 35 min

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

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

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

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

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

Answer(s): 93%