document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1140373>Question 1140373</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Working together, it takes two different sized hoses 30 minutes to fill a small swimming pool. If it takes 40 minutes for the longer hose to fill the swimming pool by itself, how long will it take the smaller hose to fill the pool on it’s own? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #760880 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=760880\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Here are two methods for solving this kind of problem that are different from the standard algebraic method suggested by the other tutor.  One is an algebraic alternative; the other uses logical reasoning.<br><BR>\n" );
document.write( "Knowing different algebraic methods for solving a problem is a good thing; but being able to solve a problem by logical reasoning is also a valuable skill.<br><BR>\n" );
document.write( "(1) algebraic alternative....<br><BR>\n" );
document.write( "Consider the least common multiple of the two given times: 120 minutes.<br><BR>\n" );
document.write( "In 120 minutes, the two hoses together could fill the pool 120/30 = 4 times; in 120 minutes the larger hose could fill the pool 120/40 = 3 times.<br><BR>\n" );
document.write( "That means the smaller hose could fill the pool 1 time in 120 minutes; and of course that means it would take the smaller hose 120 minutes to fill the pool.<br><BR>\n" );
document.write( "(2) using logical reasoning....<br><BR>\n" );
document.write( "The larger hose can fill the pool alone in 40 minutes.  So when the pool is filled by the two hoses together in 30 minutes, the larger hose itself fills 30/40 = 3/4 of the pool.<br><BR>\n" );
document.write( "That means in those 30 minutes the smaller hose fills 1/4 of the pool; and that means it would take the smaller hose 30*4 = 120 minutes to fill the pool alone. </SPAN>\n" );
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