document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=414401>Question 414401</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The speed of a plane is 120 miles/hour in a calm.  With the wind it can cover a certain distance in 4 hours, but against the wind it can cover only 3/5 of that distance in the same time.  Find the velocity of the wind.  \r<BR>\n" );
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document.write( "Here is what I got. \r<BR>\n" );
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document.write( "Let X = velocity of the wind in X miles/1 hour.\r<BR>\n" );
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document.write( "Calm:<BR>\n" );
document.write( "v = 120 miles/1 hour\r<BR>\n" );
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document.write( "Downstream:<BR>\n" );
document.write( "X miles in 4 hours, or X miles/4 hours, which is 0.25 X miles in 1 hour\r<BR>\n" );
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document.write( "Upstream:<BR>\n" );
document.write( "3/5 X miles in 4 hours, or 3/20 X miles in 1 hour\r<BR>\n" );
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document.write( "Then, <BR>\n" );
document.write( "time downstream = time upstream\r<BR>\n" );
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document.write( "distance traveled downstream / (velocity of the plane downstream + velocity of the wind) = distance traveled upstream / (velocity of the plane upstream - velocity of the wind)\r<BR>\n" );
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document.write( "0.25X miles / [{(120+X) miles}/1 hour] = 3/5X miles / [{(120-X) miles}/1 hour]\r<BR>\n" );
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document.write( "0.25X/(120+X) = 0.6X/(120-X)\r<BR>\n" );
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document.write( "0.25X (120-X) = (120+X)0.6X\r<BR>\n" );
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document.write( "Now I am stuck because I am getting X squarred. Please help. Thank you very much. \r<BR>\n" );
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document.write( "Ivana </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #290658 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=290658\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The speed of a plane is 120 miles/hour in a calm.<BR>\n" );
document.write( " With the wind it can cover a certain distance in 4 hours, but against the wind<BR>\n" );
document.write( " it can cover only 3/5 of that distance in the same time.<BR>\n" );
document.write( " Find the velocity of the wind.<BR>\n" );
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document.write( "I think you are making this more complicated than it is:<BR>\n" );
document.write( "Let x = velocity of the wind<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(120+x) = effective speed with the wind<BR>\n" );
document.write( "and<BR>\n" );
document.write( "(120+x) = effective speed against the wind<BR>\n" );
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document.write( "Change 3/5 to .6<BR>\n" );
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document.write( "Write a distance equation; dist = time * speed<BR>\n" );
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document.write( "\"against\" dist = .6 times \"with\" distance<BR>\n" );
document.write( "4(120-x) = .6(4(120+x)<BR>\n" );
document.write( "480 - 4x = .6(480+ 4x)<BR>\n" );
document.write( "480 - 4x = 288 + 2.4x<BR>\n" );
document.write( "480 - 288 = 2.4x + 4x<BR>\n" );
document.write( "192 = 6.4x<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=192%2F6.4 ALIGN=MIDDLE  ALT=\"192%2F6.4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = 30 mph is velocity of the wind <BR>\n" );
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document.write( "Check this by finding the actual distance for each trip<BR>\n" );
document.write( "4(120+30) = 600 mi<BR>\n" );
document.write( "4(120-30) = 360 mi<BR>\n" );
document.write( "Find the fraction that 360/600 = .6 which we would expect if we did this right </SPAN>\n" );
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