After 30 minutes into a race, Ian has run ⁶₁₃ of the route while Oliver has covered only ⁴₁₃ of the distance. Ian runs at the same average speed throughout the race and Oliver’s average speed is 42 m/min slower than Ian’s. If Oliver wants to finish the race at the same time as Ian, 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 Ian ran more than Oliver in first 30 min
= 30 x 42
= 1260 m

Fraction of the entire distance that was covered by Ian more than Oliver 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 Oliver ran in the first 30 min
= 4 x 630
= 2520 m

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

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

Fraction of the journey that Ian 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 Ian would take to complete
= 4410 ÷ 126
= 35 min

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

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

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

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

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

Answer(s): 93%