Question 1170603
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(1) An informal solution, using a bit of insight with logical reasoning and simple arithmetic....<br>
If the time required for the second pipe to fill the tank were also 4 hours, then the two pipes together could fill the tank in half the time, which is 2 hours.  Since 2 hours working together is 2 hours less than the 4 hours for the second pipe alone, this satisfies the conditions of the problem.<br>
ANSWER: 4 hours<br>
(2) If a formal algebraic solution is requires....<br>
Let x be the number of hours the second pipe takes to fill the tank alone.<br>
Then the fraction of the tank filled by the first pipe in 1 hour is 1/4; the fraction filled by the second pipe in 1 hour is 1/x; and the fraction filled by both pipes together in 1 hour is 1/(x-2).  So<br>
{{{1/4+1/x = 1/(x-2)}}}<br>
Multiply the whole equation by the common denominator, {{{4(x)(x-2)}}}:<br>
{{{x(x-2)+4(x-2) = 4x}}}
{{{x^2-2x+4x-8 = 4x}}}
{{{x^2-2x-8 = 0}}}
{{{(x-4)(x+2) = 0}}}
{{{x = 4}}} or {{{x = -2}}}<br>
Clearly the negative solution makes no sense in the problem, so the answer is x=4 hours.<br>