document.write( "Question 698362: A train was late by 3 hours.It had to cover a distance of 900 km. To cover the time, the driver increased the speed by 15 kmph.Find the increased speed of the train \n" ); document.write( "

Algebra.Com's Answer #430701 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
Call the increased speed $\"+s+%2B+15+\"$
\n" ); document.write( "With speed $\"+s+\"$ , time is $\"+t+%2B+3+\"$
\n" ); document.write( "where $\"+t+\"$ is on time
\n" ); document.write( "---------------------
\n" ); document.write( "Equation being late by 3 hrs:
\n" ); document.write( "(1) $\"+900+=+s%2A%28+t+%2B+3+%29+\"$
\n" ); document.write( "Equation for being on time:
\n" ); document.write( "(2) $\"+900+=+%28+s+%2B+15+%29%2At+\"$
\n" ); document.write( "-----------------------
\n" ); document.write( "(1) $\"+900+=+s%2At+%2B+3s+\"$
\n" ); document.write( "(1) $\"+s%2At+=+900+-+3s+\"$
\n" ); document.write( "(1) $\"+t+=+%28+900+-+3s+%29+%2F+s+\"$
\n" ); document.write( "Substitute (1) into (2)
\n" ); document.write( "(2) $\"+900+=+%28+s+%2B+15+%29%2A%28+900+-+3s+%29+%2F+s+\"$
\n" ); document.write( "(2) $\"+900s+=+%28+s+%2B+15+%29%2A%28+900+-+3s+%29+\"$
\n" ); document.write( "(2) $\"+900s+=+900s+%2B+13500+-+3s%5E2+-+45s+\"$
\n" ); document.write( "(2) $\"+3s%5E2+%2B+45s+-+13500+=+0+\"$
\n" ); document.write( "(2) $\"+s%5E2++%2B+15s+-+4500+=+0+\"$
\n" ); document.write( "Use quadratic formula
\n" ); document.write( " $\"+s+=+%28+-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+\"$
\n" ); document.write( " $\"+a+=+1+\"$
\n" ); document.write( " $\"+b+=+15+\"$
\n" ); document.write( " $\"+c+=+-4500+\"$
\n" ); document.write( " $\"+s+=+%28+-15+%2B-+sqrt%28+15%5E2+-+4%2A1%2A%28-4500%29+%29%29+%2F+%282%2A1%29+\"$
\n" ); document.write( " $\"+s+=+%28+-15+%2B-+sqrt%28+225+%2B+18000+%29%29+%2F+2+\"$
\n" ); document.write( " $\"+s+=+%28+-15+%2B-+sqrt%28+18225+%29%29+%2F+2+\"$ ( ignore the (-) square root )
\n" ); document.write( " $\"+s+=+%28+-15+%2B+135%29+%2F+2+\"$
\n" ); document.write( " $\"+s+=+120%2F2+\"$
\n" ); document.write( " $\"+s+=+60+\"$
\n" ); document.write( " $\"+s+%2B+15+=+75+\"$
\n" ); document.write( "The increased speed of the train is 75 km/hr
\n" ); document.write( "check:
\n" ); document.write( "(1) $\"+900+=+60%2A%28+t+%2B+3+%29+\"$
\n" ); document.write( "(1) $\"+t+%2B+3+=+15+\"$
\n" ); document.write( "(1) $\"+t+=+12+\"$
\n" ); document.write( "and
\n" ); document.write( "(2) $\"+900+=+%28+60+%2B+15+%29%2A12+\"$
\n" ); document.write( "(2) $\"+900+=+75%2A12+\"$
\n" ); document.write( "(2) $\"+900+=+900+\"$
\n" ); document.write( "OK\r
\n" ); document.write( "\n" ); document.write( " \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );