After 35 minutes into a race, Henry has run ⁷₁₃ of the route while Justin has covered only ⁴₁₃ of the distance. Henry runs at the same average speed throughout the race and Justin’s average speed is 42 m/min slower than Henry’s. If Justin wants to finish the race at the same time as Henry, 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 Henry ran more than Justin in first 35 min
= 35 x 42
= 1470 m

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

³₁₃ of the entire distance = 1470 m
¹₁₃ of the entire distance = 1470 ÷ 3 = 490 m

Distance that Justin ran in the first 35 min
= 4 x 490
= 1960 m

Justin's average speed
= 1960 ÷ 35
= 56 m/min

Henry's average speed
= 56 + 42
= 98 m/min

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

¹₁₃ of the entire distance = 490 m
⁶₁₃ of the entire distance = 6 x 490 = 2940 m

Duration that Henry would take to complete
= 2940 ÷ 98
= 30 min

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

⁹₁₃ of the entire distance = 9 x 490 = 4410 m  

Speed that Justin needs to take to complete distance at the same time as Henry
= 4410 ÷ 30
= 147 m/min

Increase in Justin's average speed
= 147 - 56
= 91 m/min

Percentage increase in Justin's average speed
= ⁹¹₅₆ x 100%
≈ 163%

Answer(s): 163%