Question

An inlet pipe on a swimming pool can be used to fill the pool in 40 hours. The drain pipe can be used to empty the pool in 42 hours. If the pool is 23 filled and then the inlet pipe and drain pipe are opened, how long from that time will it take to fill the pool?

Answer 1

Answer:

Pool will be filled in 280 hours

Step-by-step explanation:

Inlet pipe fills in  40 hours = 1 pool

Inlet pipe fills in 1 hours = $\frac{1}{40}$

Drain pipe empty in 42 hours = 1 pool

Drain pipe empty in 1 hour =  $\frac{1}{42}$

If both pipes are opened together

 then in pool fills in 1 hour =  $\frac{1}{40}$ -  $\frac{1}{42}$

      on simplifying the right side ,we get  $\frac{42-40}{(40)(42)}$

                                                                 =      $\frac{2}{(40)(42)}$

                                                                 =     $\frac{1}{840}$

      $\frac{1}{840}$  pool fills in 1 hour

                       1 pool will be filled in 840 hours

    $\frac{2}{3}$     pool is filled

empty pool =  1 - $\frac{2}{3}$ =  $\frac{1}{3}$

therfore  $\frac{1}{3}$ pool will be filled in     $\frac{1}{3}$X 840 =

                                                                                           = 280 hours