After 30 minutes into a race, Ivan has run ⁵₁₁ of the route while Ben has covered only ²₁₁ of the distance. Ivan runs at the same average speed throughout the race and Ben’s average speed is 78 m/min slower than Ivan’s. If Ben wants to finish the race at the same time as Ivan, 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 Ivan ran more than Ben in first 30 min
= 30 x 78
= 2340 m

Fraction of the entire distance that was covered by Ivan more than Ben in the first 30 min
= ⁵₁₁ - ²₁₁
= ³₁₁

³₁₁ of the entire distance = 2340 m
¹₁₁ of the entire distance = 2340 ÷ 3 = 780 m

Distance that Ben ran in the first 30 min
= 2 x 780
= 1560 m

Ben's average speed
= 1560 ÷ 30
= 52 m/min

Ivan's average speed
= 52 + 78
= 130 m/min

Fraction of the journey that Ivan needed to run to complete the race
= 1 - ⁵₁₁
= ⁶₁₁

¹₁₁ of the entire distance = 780 m
⁶₁₁ of the entire distance = 6 x 780 = 4680 m

Duration that Ivan would take to complete
= 4680 ÷ 130
= 36 min

Fraction of the journey that Ivan needed to run to complete the race
= 1 - ²₁₁
= ⁹₁₁

⁹₁₁ of the entire distance = 9 x 780 = 7020 m  

Speed that Ben needs to take to complete distance at the same time as Ivan
= 7020 ÷ 36
= 195 m/min

Increase in Ben's average speed
= 195 - 52
= 143 m/min

Percentage increase in Ben's average speed
= ¹⁴³₅₂ x 100%
≈ 275%

Answer(s): 275%