document.write( "Question 1131120: \"Julio intends to drive his motorbike to a friend's house 200 kilometers away. If he increases his planned rate of speed by 10km/hr, he can decrease his travel time by 40 minutes. What is his planned rate of speed?\" \r
\n" ); document.write( "\n" ); document.write( "I made a RxT=D chart and I had an original rate and a new rate.\r
\n" ); document.write( "\n" ); document.write( "Original Rate | R = x - 10 | T = 200/(x-10) | D = 200\r
\n" ); document.write( "\n" ); document.write( "New Rate | R = x + 10 | T = 200/(x+10) | D = 200\r
\n" ); document.write( "\n" ); document.write( "I feel like I filled out the chart a bit off and thus resulting in solving my problem wrong. (I wasn't able to multiply & distribute all the way through so I didn't get an answer) \n" ); document.write( "

Algebra.Com's Answer #747731 by ikleyn(52906) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "Julio intends to drive his motorbike to a friend's house 200 kilometers away. If he increases his planned rate $\"highlight%28cross%28of_speed%29%29\"$
\n" ); document.write( "by 10km/hr, he can decrease his travel time by 40 minutes. What is his planned rate ? $\"highlight%28cross%28of+speed%29%29\"$
\n" ); document.write( "~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "            (!) NEVER say \"rate of speed\" (!) \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "            THERE IS NO such a term.   It DOES NOT EXIST and is NEVER USED (!)\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "            As soon as you use it, you demonstrate that you are not familiar with the correct usage of the terms in the subject !\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "Let x be the planned rate in kilometers per hour. \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The the hypothetical speed is (x+10) kilometer per hour\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The planned time is   hours.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The hypothetical time is    hours.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The difference is  40 minutes, which is   of an hour.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "It gives you an equation\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     -  = .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "It is your basic equation, and when you got it, you completed the setup.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "To solve the equation, multiply its both sides by 3*x*(x+10). You will get\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    600*(x+10) - 600x = 2x*(x+10),\r\n" );
document.write( "\r\n" );
document.write( "    600x + 6000 - 600x = 2x^2 + 20x\r\n" );
document.write( "\r\n" );
document.write( "    2x^2 + 20x - 6000 = 0\r\n" );
document.write( "\r\n" );
document.write( "    x^2 + 10x - 3000 = 0\r\n" );
document.write( "\r\n" );
document.write( "    (x+60)*(x-50) = 0.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Only positive root x= 50 is meaningful.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The answer is: the planned speed is  50 kilometers per hour.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "---------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "To find many other similar solved problems, look into the lessons\r
\n" ); document.write( "\n" ); document.write( "    - Selected Travel and Distance problems from the archive \r
\n" ); document.write( "\n" ); document.write( "    - Had a car move faster it would arrive sooner\r
\n" ); document.write( "\n" ); document.write( "    - How far do you live from school? \r
\n" ); document.write( "\n" ); document.write( "in this site.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );