Question

A fish tank can be filled in 10 minutes using both pumps A and B simultaneously however pump B can pump water in OR out at the same rate if pump B is inadvertently run in reverse​

Answer 1

Answer:

A fish tank can be filled in 10 minutes using both pumps A and B simultaneously however pump B can pump water in OR out at the same rate if pump B is inadvertently run in reverse then it take 30 mins

Time taken by A alone = 15 min

Step-by-step explanation:

complete question is if B run reverse then time taken = 30 min

Let Say A alone take  = A mins

Then tank filled by A in 1 min =  1/A

Tank filled by A & B together in 1 min = 1/10

tank filled by B alone in 1 Min = 1/10 - 1/A  =  (A-10)/10A

if B id reversed then both takes 30 min

means tank filled in 1 min = 1/10

1/A - (A-10)/10A = 1/30

multiplying by 30A both sides

=> 30 - (3A-30) = A

=>  60 = 4A

=> A = 15

A alone will take 15Mins

Answer 2

Answer:

Step-by-step 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 = $Determinant \left|\begin{array}{cc}1&1\\1&-1\\\end{array}\right|$

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

                             = -2 ≠0

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

   = -4/30

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

    = -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