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

Fraction of the entire distance that was covered by Simon more than Albert 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 Albert ran in the first 35 min
= 4 x 490
= 1960 m

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

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

Fraction of the journey that Simon 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 Simon would take to complete
= 2940 ÷ 98
= 30 min

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

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

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

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

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

Answer(s): 163%