After 35 minutes into a race, Nick has run ⁵₁₁ of the route while David has covered only ³₁₁ of the distance. Nick runs at the same average speed throughout the race and David’s average speed is 96 m/min slower than Nick’s. If David wants to finish the race at the same time as Nick, 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 Nick ran more than David in first 35 min
= 35 x 96
= 3360 m

Fraction of the entire distance that was covered by Nick more than David in the first 35 min
= ⁵₁₁ - ³₁₁
= ²₁₁

²₁₁ of the entire distance = 3360 m
¹₁₁ of the entire distance = 3360 ÷ 2 = 1680 m

Distance that David ran in the first 35 min
= 3 x 1680
= 5040 m

David's average speed
= 5040 ÷ 35
= 144 m/min

Nick's average speed
= 144 + 96
= 240 m/min

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

¹₁₁ of the entire distance = 1680 m
⁶₁₁ of the entire distance = 6 x 1680 = 10080 m

Duration that Nick would take to complete
= 10080 ÷ 240
= 42 min

Fraction of the journey that Nick needed to run to complete the race
= 1 - ³₁₁
= ⁸₁₁

⁸₁₁ of the entire distance = 8 x 1680 = 13440 m  

Speed that David needs to take to complete distance at the same time as Nick
= 13440 ÷ 42
= 320 m/min

Increase in David's average speed
= 320 - 144
= 176 m/min

Percentage increase in David's average speed
= ¹⁷⁶₁₄₄ x 100%
≈ 122%

Answer(s): 122%