Quadratic Equations

Given 2 8/11 = 30/11

Let q₁, q₂ be the flow rates from two pipes, and cistern volume be V.

t₁ = V/q₁ and t₂ = V/q₂

t₁ + 1 = t₂              ..... given than one pipe takes 1 min more to fill the cistern.

t = V/(q₁ + q₂)             ... time to fill the cistern together.

30/11 = V/(q₁ + q₂)

30/11 = 1/(q₁/V + q₂/V)

30/11 = 1/(1/t₁ + 1/(t₁ + 1))

30/11 = t₁(t₁ + 1)/(2t₁ + 1)

60t₁/11 + 30/11 = t₁(t₁ + 1)

60t₁/11 + 30/11 = t₁² + t₁

t₁² - 49t₁/11 - 30/11 = 0

Solving this quadratic equation we find,

t₁ = (49/11 ± 61/11)/2

t₁ = 110/22 = 5 min and hence t₂ = 6 min.

Hence the times in which each pipe will fill the cistern are 5 and 6 min respectively.

Regards,

Team,

TopperLearning.