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

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

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

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

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

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

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

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

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

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

Answer(s): 93%