Question 1132877
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There are many ways to set up the problem to be solved algebraically; and there are many different ways to solve the system of equations that leads to the answers.<br>
The following is one path to the solution; perhaps other tutors will show very different paths.<br>
Let x be the fraction of the pool filled in 1 hour by the larger pipe and y be the fraction filled in 1 hour by the smaller pipe.  Then<br>
{{{24x+24y = 1}}}   [the two pipes together for 24 hours fill the whole pool]; and
{{{8x+18y = 1/2}}}  [the larger pipe for 8 hours, plus the smaller pipe for 18 hours, fills 1/2 of the pool]<br>
With the two equations in this form I would solve the system by elimination.  Multiplying the second equation by 3 gives us<br>
{{{24x+54y = 3/2}}}<br>
Then comparing it to the first equation (that is, subtracting one equation from the other) gives<br>
{{{30y = 1/2}}}
{{{y = 1/60}}}<br>
So the smaller pipe fills 1/60 of the pool in 1 hour, which means it takes 60 hours to fill the pool by itself.<br>
Then substitute this value for y in either of the original equation to solve for x:<br>
{{{24x+24/60 = 1}}}
{{{24x+2/5 = 5/5}}}
{{{24x = 3/5}}}
{{{x = 3/120 = 1/40}}}<br>
So the larger pipe fills 1/40 of the pool in 1 hour, which means it takes 40 hours to fill the pool by itself.