document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1202892>Question 1202892</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Officials begin to release water from a full man-made lake at a rate that would empty the lake in 12<BR>\n" );
document.write( " weeks, but a river that can fill the lake in 20<BR>\n" );
document.write( " weeks is replenishing the lake at the same time. How many weeks does it take to empty the lake? Express your answer as a fraction reduced to lowest terms, if needed.<BR>\n" );
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document.write( "Answer:  <font color=red size=4>30 weeks</font>\r<BR>\n" );
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document.write( "Explanation:\r<BR>\n" );
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document.write( "The capacity of the lake does not matter.<BR>\n" );
document.write( "Let's say the capacity is 240 thousand gallons.<BR>\n" );
document.write( "I picked this value because 12*20 = 240. Then I tacked on \"thousand\" to make the lake capacity seem more realistic.\r<BR>\n" );
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document.write( "The lake can be fully drained in 12 weeks.<BR>\n" );
document.write( "The drain rate is 240/12 = 20 thousand gallons per week.<BR>\n" );
document.write( "The fill rate is 240/20 = 12 thousand gallons per week.\r<BR>\n" );
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document.write( "This is a difference of 20-12 = 8 thousand gallons per week.<BR>\n" );
document.write( "Therefore, the net effect is the lake loses 8 thousand gallons per week even when water flows into the lake from the river. <BR>\n" );
document.write( "The faster drain rate wins overall.\r<BR>\n" );
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document.write( "x = number of weeks to drain the lake<BR>\n" );
document.write( "8000x = number of gallons drained after x weeks<BR>\n" );
document.write( "8000x = 240,000<BR>\n" );
document.write( "x = (240,000)/8000<BR>\n" );
document.write( "x = 30\r<BR>\n" );
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document.write( "It takes 30 weeks to drain the lake.<BR>\n" );
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