Question

Drains A and B are used to empty a swimming pool. Drain A alone can empty the pool in 4.75 hours. How long will it take drain B alone to empty the pool if it takes 2.6 hours when both drains are turned on?

Answer 1

B alone can empty the pool in 5.744 hours, if A alone can empty the pool in 4.75 hours and  it takes 2.6 hours when both drains are turned on.

Step-by-step explanation:

The given is,

                   A alone can empty the pool in 4.75 hours.

                   It takes 2.6 hours when both drains are turned on.

Step:1

            One hour work drains A and B =

                  One hour work of drain A + One hour work of Drain B.........(1)

            One hour work of Drain A = $\frac{1}{4.75}$

                     One hour of ( A + B ) = $\frac{1}{2.6}$

            Equation (1) becomes,

                     One hour work of B = One hour work of ( A + B )

                                                                  - One hour work of A

            Substitute the values,

                     One hour work of B =  $\frac{1}{2.6} - \frac{1}{4.75}$

                                                       = $\frac{4.75-2.6}{(4.75)(2.6)}$

                                                       = $\frac{2.15}{12.35}$

                                                       = $\frac{1}{5.744}$

                    One hour work of B  = $\frac{1}{5.744}$

             B alone can empty the pool in 5.744 hours

Result:

           B alone can empty the pool in 5.744 hours, if A alone can empty the pool in 4.75 hours and  it takes 2.6 hours when both drains are turned on.