After 25 minutes into a race, Harry has run ⁵₁₁ of the route while Julian has covered only ³₁₁ of the distance. Harry runs at the same average speed throughout the race and Julian’s average speed is 78 m/min slower than Harry’s. If Julian wants to finish the race at the same time as Harry, 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 Harry ran more than Julian in first 25 min
= 25 x 78
= 1950 m

Fraction of the entire distance that was covered by Harry more than Julian in the first 25 min
= ⁵₁₁ - ³₁₁
= ²₁₁

²₁₁ of the entire distance = 1950 m
¹₁₁ of the entire distance = 1950 ÷ 2 = 975 m

Distance that Julian ran in the first 25 min
= 3 x 975
= 2925 m

Julian's average speed
= 2925 ÷ 25
= 117 m/min

Harry's average speed
= 117 + 78
= 195 m/min

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

¹₁₁ of the entire distance = 975 m
⁶₁₁ of the entire distance = 6 x 975 = 5850 m

Duration that Harry would take to complete
= 5850 ÷ 195
= 30 min

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

⁸₁₁ of the entire distance = 8 x 975 = 7800 m  

Speed that Julian needs to take to complete distance at the same time as Harry
= 7800 ÷ 30
= 260 m/min

Increase in Julian's average speed
= 260 - 117
= 143 m/min

Percentage increase in Julian's average speed
= ¹⁴³₁₁₇ x 100%
≈ 122%

Answer(s): 122%