document.write( "Question 1154666: Hi\r
\n" ); document.write( "\n" ); document.write( "A person covers 2/3 of his journey at his usual speed and the remaining distance at 3/4 of the usual speed and takes 30min more than the usual time. If total distance is 180km what is the usual speed. \r
\n" ); document.write( "\n" ); document.write( "Thanks \n" ); document.write( "

Algebra.Com's Answer #777138 by math_helper(2461) $\"\"$ $\"About$

You can put this solution on YOUR website!


\n" );
document.write( "Make use of distance = rate * time:
\n" );
document.write( "d = r*t \r
\n" );
document.write( "\n" );
document.write( "where we solve for t:
\n" );
document.write( "t = d/r  \r
\n" );
document.write( "
\n" );
document.write( "\n" );
document.write( "Notation
\n" );
document.write( " = usual speed
\n" );
document.write( " = usual time\r
\n" );
document.write( "\n" );
document.write( "  (1) (time in hours)\r
\n" );
document.write( "\n" );
document.write( "So far, one equation with two unknowns.  We find the 2nd equation by noting equation for the usual speed:
\n" );
document.write( "   (2)\r
\n" );
document.write( "\n" );
document.write( "From here, substitute the LHS of (2) into the RHS of (1) and solve to get:
\n" );
document.write( "\r
\n" );
document.write( "
\n" );
document.write( "\n" );
document.write( "Check:
\n" );
document.write( "180km/(40km/hr) = 4.5hrs (the usual time)\r
\n" );
document.write( "\n" );
document.write( "(2/3)(180)/40 + (1/3)(180)/((3/4)40) = 3hrs + 2hrs = 5hrs  (1/2hr longer than the usual time, so this is ok)
\n" );
document.write( " \n" );
document.write( "

\n" );