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

Fraction of the entire distance that was covered by Gabriel more than Elijah 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 Elijah ran in the first 35 min
= 4 x 1190
= 4760 m

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

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

Fraction of the journey that Gabriel 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 Gabriel would take to complete
= 7140 ÷ 238
= 30 min

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

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

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

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

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

Answer(s): 163%