document.write( "Question 203098: 3 girls, Laura, Tammy, and Jeri can wash the car, clean the pool, and mow the lawn in 1 hour and 20 minutes. If Jeri did all the work, she would take twice as long as Tammy and 2 hours longer than Laura. How long would each girl take to do the job alone? \n" ); document.write( "
Algebra.Com's Answer #153236 by ankor@dixie-net.com(22740)\"\" \"About 
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3 girls, Laura, Tammy, and Jeri can wash the car, clean the pool,
\n" ); document.write( " and mow the lawn in 1 hour and 20 minutes.
\n" ); document.write( "If Jeri did all the work, she would take twice as long as Tammy and
\n" ); document.write( " 2 hours longer than Laura.
\n" ); document.write( "How long would each girl take to do the job alone?
\n" ); document.write( ":\r
\n" ); document.write( "\n" ); document.write( "Use minutes for the time: 1 hr 20 min = 80 min; 2 hr = 120 min
\n" ); document.write( ":
\n" ); document.write( "let x = time required by Tammy alone
\n" ); document.write( "then
\n" ); document.write( "2x = Jeri's time alone
\n" ); document.write( "and
\n" ); document.write( "(2x-120) = Laura's time alone (2hrs less than Jeri)
\n" ); document.write( ":
\n" ); document.write( "let the completed job = 1 (includes all three tasks
\n" ); document.write( ":
\n" ); document.write( "\"80%2Fx\" + \"80%2F%282x%29\" + \"80%2F%28%282x-120%29%29\" = 1
\n" ); document.write( "Multiply equation by 2x(2x-120) to clear the denominators
\n" ); document.write( "80(2(2x-120) + 80(2x-120) + 80(2x) = 2x(2x-120)
\n" ); document.write( ":
\n" ); document.write( "320x - 19200 + 160x - 9600 + 160x = 4x^2 - 240x
\n" ); document.write( ":
\n" ); document.write( "320x + 160x + 160x - 19200 - 9600 = 4x^2 - 240x
\n" ); document.write( ":
\n" ); document.write( "640x - 28800 = 4x^2 - 240x
\n" ); document.write( ":
\n" ); document.write( "0 = 4x^2 - 240x - 640x + 28800
\n" ); document.write( ":
\n" ); document.write( "0 = 4x^2 - 880x + 28800
\n" ); document.write( "Simplify, divide by 4
\n" ); document.write( "x^2 - 220x + 7200 = 0
\n" ); document.write( "Factor:
\n" ); document.write( "(x - 40)(x - 180) = 0
\n" ); document.write( "Two solutions,
\n" ); document.write( "x = 40; does not make sense
\n" ); document.write( "therefore
\n" ); document.write( "x = 180 min, (3 hrs) is Tammy's time alone
\n" ); document.write( "then
\n" ); document.write( "2*180 = 360 min, (6 hrs) is Jeri's time alone
\n" ); document.write( "and
\n" ); document.write( "360 - 120 = 240 min, (4 hrs) is Laura's time
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\n" ); document.write( ";
\n" ); document.write( "Check solution using 1.33 hr working together
\n" ); document.write( "1.33/3 + 1.33/6 + 1.33/4
\n" ); document.write( ".44 + .22 + .33 = .99 ~ 1 \n" ); document.write( "
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