document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=85129>Question 85129</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Sorry there is no ISBN of this textook.<BR>\n" );
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document.write( "1. A, B, and C can finish a job in 6 days. If B & C work together, the job will take 9 days; if A and C work together, the job will take 8 days. In how many days can each man working alone do the job?\r<BR>\n" );
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document.write( "2. A bicyclist and a hiker leave at the same place at the same time and travel in the same direction. The bicyclist travel three times as fast as the hiker. at the end of 3 hr they are 24 miles apart. how fast does the hiker travel.\r<BR>\n" );
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document.write( "3. A person travelling 4 hr by plane and 25 hr by ship covers 1580 miles. If the speed of the plane had been one-half of the actual speed and the speed of the ship had been one-fourth greater, the person would have travelled only 1315<BR>\n" );
document.write( "miles in the same length of time. Find the speed of the plane and the ship.\r<BR>\n" );
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document.write( "Thank you so much.\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #61501 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=61501\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. A, B, and C can finish a job in 6 days. If B & C work together, the job will take 9 days; if A and C work together, the job will take 8 days. In how many days can each man working alone do the job?<BR>\n" );
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document.write( "I was confident that the all solutions would be integers, but it was not the case with c; Here's what I got, using 3 equations:<BR>\n" );
document.write( "Let the completed job = 1<BR>\n" );
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document.write( "Eq1: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2Fa+%2B+6%2Fb+%2B+6%2Fc ALIGN=MIDDLE  ALT=\"6%2Fa+%2B+6%2Fb+%2B+6%2Fc\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
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document.write( "Eq2: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2Fb+%2B+9%2Fc ALIGN=MIDDLE  ALT=\"9%2Fb+%2B+9%2Fc\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
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document.write( "Eq3: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2Fa+%2B+8%2Fc ALIGN=MIDDLE  ALT=\"8%2Fa+%2B+8%2Fc\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
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document.write( "Find b in terms of c using eq2:<BR>\n" );
document.write( "9c + 9b = bc; multiplied thru by bc<BR>\n" );
document.write( "9b - bc = -9c<BR>\n" );
document.write( "b(9-c) = -9c<BR>\n" );
document.write( "b = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-9c%2F%289-c%29 ALIGN=MIDDLE  ALT=\"-9c%2F%289-c%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Find a in terms of c using eq3:<BR>\n" );
document.write( "8c + 8a = ac; multiplied thru by ac<BR>\n" );
document.write( "8a - ac = -8c<BR>\n" );
document.write( "a(8-c) = -8c<BR>\n" );
document.write( "a = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8c%2F%288-c%29 ALIGN=MIDDLE  ALT=\"-8c%2F%288-c%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Substitute for a and b in eq1 (invert and multiply the dividing fraction):<BR>\n" );
document.write( "6<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%288-c%29%2F%28-8c%29%29 ALIGN=MIDDLE  ALT=\"%28%288-c%29%2F%28-8c%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + 6<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%289-c%29%2F%28-9c%29%29 ALIGN=MIDDLE  ALT=\"%28%289-c%29%2F%28-9c%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2Fc ALIGN=MIDDLE  ALT=\"6%2Fc\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%2848-6c%29%2F%28-8c%29%29 ALIGN=MIDDLE  ALT=\"%28%2848-6c%29%2F%28-8c%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%2854-6c%29%2F%28-9c%29%29 ALIGN=MIDDLE  ALT=\"%28%2854-6c%29%2F%28-9c%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2Fc ALIGN=MIDDLE  ALT=\"6%2Fc\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
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document.write( "Multiply thru by 72c, get rid of the denominators and you have:<BR>\n" );
document.write( "-9(48-6c) + -8(54-6c) + 72(6) = 72c<BR>\n" );
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document.write( "-432 + 54c - 432 + 48c + 432 = 72c<BR>\n" );
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document.write( "54c + 48c - 72c - 432 - 432 + 432 = 0 <BR>\n" );
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document.write( "30c - 432 = <BR>\n" );
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document.write( "30c = +432<BR>\n" );
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document.write( "c = 432/30<BR>\n" );
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document.write( "c = 14.4 days required for c working alone<BR>\n" );
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document.write( "Find a using: a = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8c%2F%288-c%29 ALIGN=MIDDLE  ALT=\"-8c%2F%288-c%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "a = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8%2814.4%29%2F%288-%2814.4%29%29 ALIGN=MIDDLE  ALT=\"-8%2814.4%29%2F%288-%2814.4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "a = -115.2/-6.4<BR>\n" );
document.write( "a = +18 days for a to do the job alone<BR>\n" );
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document.write( "Find b using:b = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-9c%2F%289-c%29 ALIGN=MIDDLE  ALT=\"-9c%2F%289-c%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "b = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-9%2814.4%29%2F%289-%2814.4%29%29 ALIGN=MIDDLE  ALT=\"-9%2814.4%29%2F%289-%2814.4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "b = -129.6/-5.4<BR>\n" );
document.write( "b = +24 days for b<BR>\n" );
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document.write( "We should check the solutions in each original equation:<BR>\n" );
document.write( " eq1: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2Fa+%2B+6%2Fb+%2B+6%2Fc ALIGN=MIDDLE  ALT=\"6%2Fa+%2B+6%2Fb+%2B+6%2Fc\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2F18+%2B+6%2F24+%2B+6%2F14.4 ALIGN=MIDDLE  ALT=\"6%2F18+%2B+6%2F24+%2B+6%2F14.4\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1; I used a calc<BR>\n" );
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document.write( "Try checking solutions in eq2 and eq3<BR>\n" );
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document.write( "2. A bicyclist and a hiker leave at the same place at the same time and travel in the same direction. The bicyclist travel three times as fast as the hiker. at the end of 3 hr they are 24 miles apart. how fast does the hiker travel.<BR>\n" );
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document.write( "Let s = hikers speed in mph<BR>\n" );
document.write( "Then 3s = bicyclist speed<BR>\n" );
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document.write( "Write a distance equation: dist = time * speed<BR>\n" );
document.write( "bicyclist dist - hiker dist = 24 mi<BR>\n" );
document.write( "3(3s) - 3s = 24<BR>\n" );
document.write( "9s - 3s = 24<BR>\n" );
document.write( "6s = 24<BR>\n" );
document.write( "s = 4 mph is the hikers speed, obviously the bicyclist speed the 12 mph<BR>\n" );
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document.write( "check 3(12) - 3(4) = 24<BR>\n" );
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document.write( "3. A person traveling 4 hr by plane and 25 hr by ship covers 1580 miles. If the speed of the plane had been one-half of the actual speed and the speed of the ship had been one-fourth greater, the person would have traveled only 1315<BR>\n" );
document.write( "miles in the same length of time. Find the speed of the plane and the ship.<BR>\n" );
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document.write( "let x = actual speed of the plane<BR>\n" );
document.write( "let y = actual speed of the ship<BR>\n" );
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document.write( "Dist = time * speed:<BR>\n" );
document.write( "actual: 4x + 25y = 1580<BR>\n" );
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document.write( "If equation:<BR>\n" );
document.write( ".5(4x) + 1.25(25y) = 1315<BR>\n" );
document.write( "2x + 31.25y = 1315<BR>\n" );
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document.write( "Mult above equation by 2 and subtract the actual equation:<BR>\n" );
document.write( "4x +62.5y = 2630<BR>\n" );
document.write( "4x +  25y = 1580<BR>\n" );
document.write( "------------------subtracting eliminates x<BR>\n" );
document.write( "0x + 37.5y = 1050<BR>\n" );
document.write( "y = 1050/37.5<BR>\n" );
document.write( "y = 28 mph, actual ship's speed<BR>\n" );
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document.write( "Find x using 2x + 31.25y = 1315<BR>\n" );
document.write( "2x + 31.25(28) = 1315<BR>\n" );
document.write( "2x + 875 = 1315<BR>\n" );
document.write( "2x = 1315 - 875<BR>\n" );
document.write( "x = 440/2<BR>\n" );
document.write( "x = 220 mph, actual speed of the plane<BR>\n" );
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document.write( "Check solutions in the actual equation:<BR>\n" );
document.write( "4(220) + 25(28) = <BR>\n" );
document.write( "880 + 700 = 1580\r<BR>\n" );
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