document.write( "Question 1032090: One hose can fill a tank in 1.5 hours. Another hose can fill the same tank in .75 hours. How long will it take to fill the tank if both hoses are used? \n" ); document.write( "

Algebra.Com's Answer #646751 by josmiceli(19441) $\"\"$ $\"About$

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Add their rates of filling
\n" ); document.write( "Rate for 1st hose:
\n" ); document.write( "[ 1 tank filled ] / [ 1.5 hrs ]
\n" ); document.write( "Rate for 2nd hose:
\n" ); document.write( "[ 1 tank filled ] / [ .75 hrs ]
\n" ); document.write( "-----------------------
\n" ); document.write( "Let $\"+t+\"$ = time in hrs to fill
\n" ); document.write( "the tank with both hoses
\n" ); document.write( "-----------------------
\n" ); document.write( " $\"+1%2F1.5+%2B+1%2F.75+=+1%2Ft+\"$
\n" ); document.write( "Multiply both sides by $\"+1%2F4+\"$
\n" ); document.write( " $\"+1%2F6+%2B+1%2F3++=+1%2F%284t%29+\"$
\n" ); document.write( "Multiply both sides by $\"+12t+\"$
\n" ); document.write( " $\"+2t+%2B+4t+=+3+\"$
\n" ); document.write( " $\"+6t+=+3+\"$
\n" ); document.write( " $\"+t+=+1%2F2+\"$
\n" ); document.write( "--------------
\n" ); document.write( "It will take 1/2 hr to fill tank
\n" ); document.write( "with both hoses
\n" ); document.write( "------------------------
\n" ); document.write( "check:
\n" ); document.write( " $\"+1%2F1.5+%2B+1%2F.75+=+1%2Ft+\"$
\n" ); document.write( " $\"+1%2F1.5+%2B+1%2F.75+=+1%2F.5+\"$
\n" ); document.write( " $\"+2%2F3+%2B+4%2F3+=+2+\"$
\n" ); document.write( " $\"+6%2F3+=+2+\"$
\n" ); document.write( " $\"+2+=+2+\"$
\n" ); document.write( "OK \n" ); document.write( "

\n" );