Question

A fish tank can be filled in 10minutes using both pumps A & B simultaneously. However, pump B can pump water in or out at the same rate. If pump B is inadvertently run in reverse, then the tank will be filled in 30minutes. How long it take to each pump to fill the tank by itself? (Use Cramer's rule to solve the problem)



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Answer 1

☯ Question:–

• ★ A fish tank can be filled in 10minutes using both pumps A & B simultaneously. However, pump B can pump water in or out at the same rate. If pump B is inadvertently run in reverse, then the tank will be filled in 30minutes. How long it take to each pump to fill the tank by itself? (Use Cramer's rule to solve the problem)

☯Answer with Explanation:–

Let us consider Pump A as 'x'.

Pump A filled the tank in 1 minute = 1/x

Let us consider Pump B as 'y'

Pump B filled the tank in 1 minute = 1/y

A and B together filled the tank in 1 minute = 1/x + 1/y = 1/10

Pump B reversed (or) filled the tank at the same rate = - 1/y

Therefore, 1/x - 1/y = 1/30

Put 1/x = a and 1/y = b.

a+b=1/10; a-b=1/30

Determinant = Δ = $\begin{gathered}Determinant \left|\begin{array}{cc}1&1\\1&-1\\\end{array}\right|\end{gathered}$

Determinant

= 1(-1) - (1)(1)

= -2 ≠0

Δa = $\begin{gathered}Determinant = \left|\begin{array}{cc}1/10&1\\1/30&-1\\\end{array}\right|\end{gathered}$

Determinant=

= -4/30

Δb = $\begin{gathered}Determinant \left|\begin{array}{cc}1&1/10\\1&1/30\\\end{array}\right|\end{gathered}$

Determinant

= -2/30

By Cramer's Rule,

a = Δa/Δ = 1/15

b = Δb/Δ = 1/30

Therefore, a = 1/x = 1/15

⇒ x = 15 minutes

b = 1/y = 1/30

⇒ y = 30 minutes

x = 15 minutes = Pump A, y = 30 minutes = Pump B

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