Pipe A and pipe B can fill a tank in x days. Pipe A can fill the tank in (x + 4) days and pipe B can fill the tank in (x + 36) days. How many days both pipes can fill 1/3 of the tank?

Question

Question

Answer 1

Given:

Pipe A and pipe B can fill a tank =x days

Pipe A can fill the tank = (x + 4) days

Pipe B can fill the tank = (x + 36) days.

Formula used:

Time to work together = √product of extra days

Calculation:

Pipe A and pipe B can fill the tank = √4 × 36

⇒ x = √144

⇒ x = 12 days

∴ Both pipes can fill 1/3 of the tank = 12/3 = 4 days

Alternate Method

Pipe A and pipe B can fill the tank = (t₁ × t₂)/(t₁ + t₂)

⇒ x = (x + 4) × (x + 36)/(x + 4 + x + 36)

⇒ x(2x + 40) = x² + 36x + 4x + 144

⇒ 2x² + 40x = x² + 40x + 144

⇒ x² = 144

⇒ x = 12 days

∴ Both pipes can fill 1/3 of the tank = 12/3 = 4 days