Question 1187411
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When two hoses are connected to a swimming pool, they can fill the pool in 4 hrs if both are open. 
If only the larger hose is open, it can fill the pool in 6 hrs less than the smaller hose. 
How long will it take each hose to fill the pool?
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<pre>
Let x = hours to fill, for the smaller hose.

Then the time for the larger hose to fill the pool is  (x+4)  hours.


The equation for the combined rate of work is.

    {{{1/x}}} + {{{1/(x+6)}}} = {{{1/4}}}.    (1)


To solve it, multiply both sides by 4.  You will get

    {{{4/x}}} + {{{4/(x+6)}}} = 1.     (2)


From this point, I just see the answer.  It is  x= 6 hours.


<U>CHECK</U>  equation (2).  Its left side is  {{{4/6}}} + {{{4/(6+6)}}} = {{{2/3}}} + {{{1/3}}} = 1   ! Correct !


Alternatively, you can reduce equation (2) to a quadratic equation
and solve it using the quadratic fotmula or factoring.


Knowing the answer will facilitate your job.
</pre>

Solved and explained.