document.write( "Question 132277: Machine A turns out 500 buttons in a certain number of minutes and Machine B turns out the same number of buttons in twice the time of Machine A. When both machines are used to produce 500 buttons, the time required is 40 minutes. Find the number of minutes each machine turns out 500 buttons. \n" ); document.write( "

Algebra.Com's Answer #96625 by josmiceli(19441) $\"\"$ $\"About$

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Since the problem only talks about 500 buttons and no other number
\n" ); document.write( "of buttons, I can call 500 buttons 1 job
\n" ); document.write( "(machine A's rate) + (machine B's rate) = (rate running together)
\n" ); document.write( "(1 job / x minutes) + (1 job / 2x minutes) = 1 job / 40 minutes)
\n" ); document.write( " $\"1%2Fx+%2B+1%2F%282x%29+=+1%2F40\"$
\n" ); document.write( "Multiply both sides by $\"2%2Ax%2A40\"$
\n" ); document.write( " $\"80+%2B+40+=+2x\"$
\n" ); document.write( " $\"2x+=+120\"$
\n" ); document.write( " $\"x+=+60\"$
\n" ); document.write( "Machine A makes 500 buttons in 60 minutes
\n" ); document.write( "Machine B makes 500 buttons in 120 minutes
\n" ); document.write( "check:
\n" ); document.write( " $\"1%2Fx+%2B+1%2F%282x%29+=+1%2F40\"$
\n" ); document.write( " $\"1%2F60+%2B+1%2F120+=+1%2F40\"$
\n" ); document.write( " $\"2%2F120+%2B+1%2F120+=+3%2F120\"$
\n" ); document.write( " $\"1+%2B+2+=+3\"$
\n" ); document.write( "OK \n" ); document.write( "

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