document.write( "Question 1204620: The hot water tap can fill the tub in 10 minutes. The cold water tap can fill the tub in 8 minutes. How long would it take to fill the tub if both taps are opened? \n" ); document.write( "
Algebra.Com's Answer #840980 by math_tutor2020(3817)\"\" \"About 
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\n" ); document.write( "Let's say the tub has a capacity of 10*8 = 80 gallons.
\n" ); document.write( "The capacity doesn't matter. You can pick any number you want. I'm picking this value so the unit rates are whole numbers.\r
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\n" ); document.write( "\n" ); document.write( "The hot water fills the tub in 10 minutes, so its unit rate is 80/10 = 8 gallons per minute
\n" ); document.write( "The formula I used was: rate = (amount done)/(time)
\n" ); document.write( "I'm assuming that the cold water tap isn't on.\r
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\n" ); document.write( "\n" ); document.write( "The cold water tap can fill the tub in 8 minutes, to give it a unit rate of 80/8 = 10 gallons per minute.
\n" ); document.write( "I'm assuming that the hot water tap isn't on.\r
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\n" ); document.write( "\n" ); document.write( "The combined unit rate of both hot and cold is 8+10 = 18 gallons per min.\r
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\n" ); document.write( "\n" ); document.write( "The goal is to fill the 80 gallon tub and we can do so at a combined rate of 18 gallons per minute.\r
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\n" ); document.write( "\n" ); document.write( "time = (amount done)/(rate)
\n" ); document.write( "time = 80/18
\n" ); document.write( "time = 4.44 minutes approximately\r
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\n" ); document.write( "\n" ); document.write( "An alternative, and perhaps the standard textbook way to solve rates problems like this, is to solve the equation \"1%2F10+%2B+1%2F8+=+1%2Fx\", but this method may be a bit cryptic and not that intuitive (in my opinion).
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