After 35 minutes into a race, Rael has run ⁷₁₃ of the route while Ahmad has covered only ⁴₁₃ of the distance. Rael runs at the same average speed throughout the race and Ahmad’s average speed is 96 m/min slower than Rael’s. If Ahmad wants to finish the race at the same time as Rael, 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 Rael ran more than Ahmad in first 35 min
= 35 x 96
= 3360 m

Fraction of the entire distance that was covered by Rael more than Ahmad in the first 35 min
= ⁷₁₃ - ⁴₁₃
= ³₁₃

³₁₃ of the entire distance = 3360 m
¹₁₃ of the entire distance = 3360 ÷ 3 = 1120 m

Distance that Ahmad ran in the first 35 min
= 4 x 1120
= 4480 m

Ahmad's average speed
= 4480 ÷ 35
= 128 m/min

Rael's average speed
= 128 + 96
= 224 m/min

Fraction of the journey that Rael needed to run to complete the race
= 1 - ⁷₁₃
= ⁶₁₃

¹₁₃ of the entire distance = 1120 m
⁶₁₃ of the entire distance = 6 x 1120 = 6720 m

Duration that Rael would take to complete
= 6720 ÷ 224
= 30 min

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

⁹₁₃ of the entire distance = 9 x 1120 = 10080 m  

Speed that Ahmad needs to take to complete distance at the same time as Rael
= 10080 ÷ 30
= 336 m/min

Increase in Ahmad's average speed
= 336 - 128
= 208 m/min

Percentage increase in Ahmad's average speed
= ²⁰⁸₁₂₈ x 100%
≈ 163%

Answer(s): 163%