document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=356735>Question 356735</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A mother horse and a baby horse walk 10 miles from point A to point B. The mother’s speed is 10 miles per hour and the baby’s 5 miles per hour. The mother rests for 2 minutes after every x minutes of walking. The baby keeps walking. They arrive together at the destination. Find the range of x. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #601330 by </B><A HREF=/tutors/aboutme.mpl?userid=onlinepsa><B>onlinepsa(22)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=onlinepsa><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=onlinepsa><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=601330\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The baby horse's speed is 5 miles per hour; thus it will take 2 hours to cover a distance of 10 miles from A to B.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The mother horse's speed is 10 miles per hour; if she does not stop anywhere she should take 1 hr to reach B. But she arrives at B at the same time as the baby. Thus, she spends 1 hr of time resting.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "In an ideal situation, if she spends 2 minutes for each 'break' she would have taken 30 breaks. Thus, the one hour of walking when divided by '30' should give us x=2. Or, she does a 2 minutes of walk and then rests for 2 minutes.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "However, the above is NOT correct. [No doubt author's question is 'range of x' and NOT 'value of x']\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Her walking & resting forms the pattern - W, R, W, R, W , R ....\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Think about the answer to the question - What does she do at last- 'W' [for walking] or 'R' [for resting]? Invariably our above method says, she already reached B and then rested for '2 minutes' at B after which the baby arrives. This violates \"They arrive together at the destination\".\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We must notice that the number of breaks will be one less than total number of 'walks'; the last should be 'W' when she reaches B.<BR>\n" );
document.write( "[As in W, R, W or W, R, W, R, W and so on].\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Let the number of 'walks' be 'b' where each 'walk' is of 'x' minutes; therefore, the number of breaks [of 2 minutes] will be b-1.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "According to the question,\r<BR>\n" );
document.write( "\n" );
document.write( "b*x+ (b-1)*2=120<BR>\n" );
document.write( "bx + 2b= 122<BR>\n" );
document.write( "x=(122/b)-2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "As, we already said, number of breaks cannot be 30 or x cannot be ideally equal to '2'. It must be less than 2. Also it must be greater than 0.<BR>\n" );
document.write( "Thus, range of x is: 2>x>0.\r<BR>\n" );
document.write( "\n" );
document.write( "[Since, 'b' is an integral value we can also find out the exact number of values of x here.<BR>\n" );
document.write( "2>x>0\r<BR>\n" );
document.write( "\n" );
document.write( "=>2>(122/b)-2>0<BR>\n" );
document.write( "=>4>(122/b)> 2<BR>\n" );
document.write( "=>61> b> 30.5\r<BR>\n" );
document.write( "\n" );
document.write( "b ranges from 31 to 60; there are 30 unique values of x possible.]\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Hope this helps!\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Thanks,<BR>\n" );
document.write( "PRD<BR>\n" );
document.write( "https://onlinepsa.wordpress.com </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );