document.write( "Question 1089241: On Monday, Alberta picked the strawberry patch, and Ernie sold the berries. On Tuesday, Ernie picked and Alberta sold, but it took him 2 hours longer to get the berries picked than it took Alberta. On Wednesday they worked together and got all of the berries picked in 5 hours. How long did it take Ernie to pick the berries by himself? Find an exact answer and an approximate answer to the problem. \n" ); document.write( "

Algebra.Com's Answer #703620 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let $\"+t+\"$ = Alberta's time in hrs to pick on monday
\n" ); document.write( " $\"+t+%2B+2+\"$ = Ernie's time in hrs to pick on tuesday
\n" ); document.write( " $\"+5+\"$ = their time in hrs picking together on wednesday
\n" ); document.write( "---------------------------------------------------
\n" ); document.write( "I think what they are not telling you is that they need a
\n" ); document.write( "certain amount of berries each day, and they stop picking
\n" ); document.write( "when they get that amount. I can call that amount [ 1 load of berries ]
\n" ); document.write( "------------------------------------------------------------
\n" ); document.write( "Alberta's rate of picking:
\n" ); document.write( "[ 1 load of berries ] / [ t hrs ]
\n" ); document.write( "Ernie's rate of picking:
\n" ); document.write( "[ 1 load of berries ] / [ t + 2 hrs ]
\n" ); document.write( "Their rate of picking working together:
\n" ); document.write( "[ 1 load of berries ] / [ 5 hrs ]
\n" ); document.write( "-----------------------------------
\n" ); document.write( "Add their individual rates to get their rate working together
\n" ); document.write( " $\"+1%2Ft+%2B+1%2F%28%28+t%2B2+%29%29+=+1%2F5+\"$
\n" ); document.write( "Multiply each side by $\"+5t%2A%28+t%2B2+%29+\"$
\n" ); document.write( " $\"+5%2A%28+t+%2B+2+%29+%2B+5t+=+t%2A%28+t+%2B+2+%29+\"$
\n" ); document.write( " $\"+5t+%2B+10+%2B+5t+=+t%5E2+%2B+2t+\"$
\n" ); document.write( " $\"+10t+%2B+10+=+t%5E2+%2B+2t+\"$
\n" ); document.write( " $\"+t%5E2+-+8t+-+10+=+0+\"$
\n" ); document.write( "Complete the square
\n" ); document.write( " $\"+t%5E2+-+8t+%2B+%28-8%2F2%29%5E2+=+10+%2B+%28-8%2F2%29%5E2+\"$
\n" ); document.write( " $\"+t%5E2+-+8t+%2B+16+=+10+%2B+16+\"$
\n" ); document.write( " $\"+%28+t+-+4+%29%5E2+=+%28+sqrt%2826%29+%29%5E2+\"$
\n" ); document.write( " $\"+t+-+4+=+sqrt%2826+%29+\"$
\n" ); document.write( " $\"+t+=+4+%2B+sqrt%28+26+%29+\"$
\n" ); document.write( "This is Ernies exact time in hrs
\n" ); document.write( " $\"+sqrt%2826%29+=+5.1+\"$
\n" ); document.write( " $\"+t+=+4+%2B+5.1+\"$
\n" ); document.write( " $\"+t+=+9.1+\"$
\n" ); document.write( "Ernie's approximate time in hrs
\n" ); document.write( "---------------------------------
\n" ); document.write( "check the answer:
\n" ); document.write( " $\"+1%2Ft+%2B+1%2F%28%28+t%2B2+%29%29+=+1%2F5+\"$
\n" ); document.write( " $\"+1%2F%28%28+4+%2B+sqrt%2826%29+%29%29+%2B+1%2F%28%28+6+%2B+sqrt%2826%29+%29%29+=+1%2F5+\"$
\n" ); document.write( "

\n" ); document.write( " $\"+30+%2B+5%2Asqrt%2826%29+%2B+20+%2B+5%2Asqrt%2826%29+=+24+%2B+10%2Asqrt%2826%29+%2B+26+\"$
\n" ); document.write( " $\"+50+%2B+10%2Asqrt%2826%29+=+50+%2B+10%2Asqrt%2826%29+\"$
\n" ); document.write( "OK
\n" ); document.write( "( you can check using $\"+t+=+9.1+\"$ also )
\n" ); document.write( " \n" ); document.write( "

\n" );