document.write( "Question 853638: One hose can fill a goldfish pond in 60 minutes, and two hoses can fill the same pond in 35 minutes. How long does it take the second hose alone to fill the pond? \n" ); document.write( "

Algebra.Com's Answer #514165 by LinnW(1048) $\"\"$ $\"About$

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The first hose fills at a rate of 1/60 ponds per minute.
\n" ); document.write( "Let s = the rate at which the second fills in ponds per minute.
\n" ); document.write( "So (1/60)35 + (s)35 = 1 pond
\n" ); document.write( "35/60 + 35s = 1
\n" ); document.write( "add -35/60 to each side
\n" ); document.write( " 35s = 1 - 35/60
\n" ); document.write( " 35s = 25/60
\n" ); document.write( "Multiply each side by 1/35
\n" ); document.write( " $\"s+=+25%2F60+%2A+1%2F35\"$
\n" ); document.write( " $\"s+=+25%2F%2860%2A35%29\"$
\n" ); document.write( " $\"s+=+%285%2A5%29%2F%282%2A5%2A6%2A5%2A7%29\"$
\n" ); document.write( " $\"s+=+1%2F%282%2A6%2A7%29\"$
\n" ); document.write( " $\"s+=+1%2F84\"$
\n" ); document.write( "Let's verify that 1/84 is the correct rate.
\n" ); document.write( "(1/60 + 1/84)35 ?= 1
\n" ); document.write( "( 35/60 + 35/84 ) ?= 1
\n" ); document.write( "( (5*7)/(2*5*6) + (5*7)/(2*6*7) ) ?=1
\n" ); document.write( " ( 7/12 + 5/12 ) ?= 1
\n" ); document.write( "12/12 = 1, so the rate 1/84 pools per minute checks out
\n" ); document.write( "so it will take 84 minutes to fill the pool with the second hose. \n" ); document.write( "

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