document.write( "Question 1186764: Cyclist A travelled 60 km. Cyclist B travels 5 km/hr faster than A and travels the same distance in 2 hours less. Find the speed of each. \n" ); document.write( "

Algebra.Com's Answer #817749 by ikleyn(52776) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "Cyclist A travelled 60 km. Cyclist B travels 5 km/hr faster than A
\n" ); document.write( "and travels the same distance in 2 hours less. Find the speed of each.
\n" ); document.write( "~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " The solution by @Alan is incorrect.\r
\n" ); document.write( "\n" ); document.write( " I came to bring you a correct solution.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "Let x be the speed of cyclist A, in km/h.\r\n" );
document.write( "\r\n" );
document.write( "Then the speed of cyclist B is (x+5) km/h, according to the condition.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Cyclist A spent        hours.\r\n" );
document.write( "\r\n" );
document.write( "Cyclist B spent    hours.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The difference of times is 2 hours.   It gives you THIS \"time equation\"\r\n" );
document.write( "\r\n" );
document.write( "     -  = 2.      (1)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "        At this point, I just can to guess the answer mentally :  it is  x= 10 km/h.\r\n" );
document.write( "\r\n" );
document.write( "        But let's get it formally . . . \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "From the time equation, by multiplying both sides by x*(x+5) you get\r\n" );
document.write( "\r\n" );
document.write( "    60(x+5) - 60x = 2x*(x+5)\r\n" );
document.write( "\r\n" );
document.write( "    60x + 300 - 60x = 2x^2 + 10x\r\n" );
document.write( "\r\n" );
document.write( "          300       = 2x^2 + 10x\r\n" );
document.write( "\r\n" );
document.write( "          2x^2 + 10x - 300 = 0\r\n" );
document.write( "\r\n" );
document.write( "           x^2 +  5x - 150 = 0\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Factor left side\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "           (x-10)*(x+15) = 0\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The last equation has two roots,  10 and -15,  of which we select the positive value  x= 10.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "ANSWER.  Cyclists A  speed is 10 km/h;  Cyclist B speed is 10+5 = 15 km/h.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "CHECK.  Calculate left side of the equation (1).  It is   -  = 6 - 4 = 2  hours.  ! Correct !\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "================\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Couple of words as a conclusion.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "What I presented here, is a standard version and a standard way solving such problems using \"time equation\".\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "It is straightforward and clear. It prevents you of making mistakes.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "If you deviate from this scheme of writing the solution, and will write a mess, then NOTHING will prevent you \r
\n" ); document.write( "\n" ); document.write( "of making mistakes on the way.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );