After 35 minutes into a race, Daniel has run ⁷₁₃ of the route while Eric has covered only ⁴₁₃ of the distance. Daniel runs at the same average speed throughout the race and Eric’s average speed is 102 m/min slower than Daniel’s. If Eric wants to finish the race at the same time as Daniel, 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 Daniel ran more than Eric in first 35 min
= 35 x 102
= 3570 m

Fraction of the entire distance that was covered by Daniel more than Eric in the first 35 min
= ⁷₁₃ - ⁴₁₃
= ³₁₃

³₁₃ of the entire distance = 3570 m
¹₁₃ of the entire distance = 3570 ÷ 3 = 1190 m

Distance that Eric ran in the first 35 min
= 4 x 1190
= 4760 m

Eric's average speed
= 4760 ÷ 35
= 136 m/min

Daniel's average speed
= 136 + 102
= 238 m/min

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

¹₁₃ of the entire distance = 1190 m
⁶₁₃ of the entire distance = 6 x 1190 = 7140 m

Duration that Daniel would take to complete
= 7140 ÷ 238
= 30 min

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

⁹₁₃ of the entire distance = 9 x 1190 = 10710 m  

Speed that Eric needs to take to complete distance at the same time as Daniel
= 10710 ÷ 30
= 357 m/min

Increase in Eric's average speed
= 357 - 136
= 221 m/min

Percentage increase in Eric's average speed
= ²²¹₁₃₆ x 100%
≈ 163%

Answer(s): 163%