After 30 minutes into a race, Gabriel has run ⁶₁₃ of the route while Justin has covered only ⁴₁₃ of the distance. Gabriel runs at the same average speed throughout the race and Justin’s average speed is 42 m/min slower than Gabriel’s. If Justin 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 Justin in first 30 min
= 30 x 42
= 1260 m

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

²₁₃ of the entire distance = 1260 m
¹₁₃ of the entire distance = 1260 ÷ 2 = 630 m

Distance that Justin ran in the first 30 min
= 4 x 630
= 2520 m

Justin's average speed
= 2520 ÷ 30
= 84 m/min

Gabriel's average speed
= 84 + 42
= 126 m/min

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

¹₁₃ of the entire distance = 630 m
⁷₁₃ of the entire distance = 7 x 630 = 4410 m

Duration that Gabriel would take to complete
= 4410 ÷ 126
= 35 min

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

⁹₁₃ of the entire distance = 9 x 630 = 5670 m  

Speed that Justin needs to take to complete distance at the same time as Gabriel
= 5670 ÷ 35
= 162 m/min

Increase in Justin's average speed
= 162 - 84
= 78 m/min

Percentage increase in Justin's average speed
= ⁷⁸₈₄ x 100%
≈ 93%

Answer(s): 93%