document.write( "Question 1022114: Jenny and Penny can eat a whole gallon of ice cream together in 2 hours. Penny and Lenny can eat a whole gallon of ice cream together in 1 (2/3) hours. All three together can eat a whole gallon of ice cream together in 1 hour. How many hours would it take Jenny to eat a whole gallon of ice cream all by herself? \n" ); document.write( "

Algebra.Com's Answer #637857 by ikleyn(52803) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "The previous tutor just pointed you an approach and a way to write the equations.
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document.write( "Rates of more than one eater at the same time are additive.\r\n" );
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document.write( "j, time for Jenny\r\n" );
document.write( "p, time for Penny\r\n" );
document.write( "y, time for Lenny\r\n" );
document.write( "To eat the one gallon on each's own\r\n" );
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document.write( "Notice that the numerators in all terms are 1, and only a variable is used in every denominator on the left hand members.\r\n" );
document.write( "An alternative is to not to focus on the times as variables, but to focus on the RATES directly as variables, \r\n" );
document.write( "although each rate will still be a fraction.\r\n" );
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document.write( "You might be more comfortable reassigning new variables J = , P =  and Y =  and forming\r\n" );
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document.write( "J + P     = ,     (1)    \r\n" );
document.write( "P +     Y = ,     (2)          ( <----- 3/5 =  )\r\n" );
document.write( "J + P + Y = .     (3)\r\n" );
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document.write( "Now you have a system of LINEAR equations instead of RATIONAL equations. \r\n" );
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document.write( "Add equations (1) and (2). You will get\r\n" );
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document.write( "J + 2P + Y =  =  = .   (4)\r\n" );
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document.write( "Now distract equation (3) from (4). You will get\r\n" );
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document.write( "P =  = .   (You just have the rate for Lenny!)\r\n" );
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document.write( "Next, from (1) you get J =  - P =  =  = .\r\n" );
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document.write( "This is Jenny's rate.\r\n" );
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document.write( "Hence, it will take  =  =  =  hours for Jenny to eat a whole gallon of ice cream by herself.\r\n" );
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document.write( "The problem is solved.\r\n" );
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