document.write( "Question 885922: An oil tanker can be emptied by the main pump in 4 hours. An auxiliary pump can empty the tanker in 7 hours. If the main pump is started at 8PM, when should the auxiliary pump be started so that the tanker is emptied by 11PM? \n" ); document.write( "

Algebra.Com's Answer #535558 by josmiceli(19441) $\"\"$ $\"About$

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The rate of emptying for main pump is:
\n" ); document.write( " $\"+1%2F4+\"$ which is ( 1 tanker / 4 hrs )
\n" ); document.write( "The rate of emptying for auxiliary pump is:
\n" ); document.write( " $\"+1%2F7+\"$ which is ( 1 tanker / 7 hrs )
\n" ); document.write( "--------------------------
\n" ); document.write( "8 PM to 11 PM is $\"+3+\"$ hrs
\n" ); document.write( "Let $\"+t+\"$ = time in hrs during which main pump is on
\n" ); document.write( " $\"+3+-+t+\"$ = time in hrs during which both pumps are on
\n" ); document.write( "--------------------------
\n" ); document.write( "For main pump alone:
\n" ); document.write( "fraction of tanker emptied = $\"+%28+1%2F4%29%2At+\"$
\n" ); document.write( " $\"+1+-+%28+1%2F4+%29%2At+\"$ = fraction left to be emptied
\n" ); document.write( "--------------------------
\n" ); document.write( "With both pumps on:
\n" ); document.write( " $\"+%28+1+-+%28+1%2F4+%29%2At+%29+%2F+%28+3+-+t+%29+=+1%2F4+%2B+1%2F7+\"$
\n" ); document.write( "Multiply both sides by $\"+4%2A7%2A%28+3-t+%29+\"$
\n" ); document.write( " $\"+4%2A7%2A%28+1+-+%28+1%2F4+%29%2At+%29+=+7%2A%28+3+-+t+%29+%2B+4%2A%28+3+-+t+%29+\"$
\n" ); document.write( " $\"+28%2A%28+1+-+%281%2F4%29%2At+%29+=+21+-+7t+%2B+12+-+4t+\"$
\n" ); document.write( " $\"+28+-+7t+=+21+-+7t+%2B+12+-+4t+\"$
\n" ); document.write( " $\"+28+=+33+-+4t+\"$
\n" ); document.write( " $\"+4t+=+5+\"$
\n" ); document.write( " $\"+t+=+1.25+\"$
\n" ); document.write( "----------------
\n" ); document.write( "The auxiliary pump should be started at:
\n" ); document.write( "8 PM + 1.25 hrs = 9:15 PM
\n" ); document.write( "------------------------
\n" ); document.write( "check:
\n" ); document.write( " $\"+%28+1+-+%28+1%2F4+%29%2At+%29+%2F+%28+3+-+t+%29+=+1%2F4+%2B+1%2F7+\"$
\n" ); document.write( " $\"+%28+1+-+%28+1%2F4+%29%2A%285%2F4%29+%29+%2F+%28+3+-+5%2F4+%29+=+1%2F4+%2B+1%2F7+\"$
\n" ); document.write( " $\"+%28+1+-+5%2F16+%29+%2F+%28+7%2F4+%29+=+7%2F28+%2B+4%2F28+\"$
\n" ); document.write( " $\"+%28+11%2F16+%29+%2F+%28+7%2F4+%29+=+11%2F28+\"$
\n" ); document.write( " $\"+%28+11%2F16+%29%2A%28+4%2F7+%29+=+11%2F28+\"$
\n" ); document.write( " $\"+11%2F28+=+11%2F28+\"$
\n" ); document.write( "OK
\n" ); document.write( " \r
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