document.write( "Question 1024592: Carlos takes 15 minutes longer than Amy does to make the 110-mile drive between two cities. Amy drives 4 miles an hour faster. How fast do Carlos and Amy drive? \n" ); document.write( "

Algebra.Com's Answer #640005 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let $\"+s+\"$ = Carlos's speed in mi/hr
\n" ); document.write( " $\"+s+%2B+4+\"$ = Amy's speed in mi/hr
\n" ); document.write( "Let $\"+t+\"$ = Amy's driving time in hrs
\n" ); document.write( " $\"+t+%2B+1%2F4+\"$ = Carlos's time in hrs ( 15 min = 1/4 hr )
\n" ); document.write( "-----------------------
\n" ); document.write( "Carlos's equation:
\n" ); document.write( "(1) $\"+110+=+s%2A%28+t+%2B+1%2F4+%29+\"$
\n" ); document.write( "Amy's equation:
\n" ); document.write( "(2) $\"+110+=+%28+s+%2B+4+%29%2At+\"$
\n" ); document.write( "------------------------
\n" ); document.write( "(2) $\"+t+=+110+%2F+%28+s%2B4+%29+\"$
\n" ); document.write( "and
\n" ); document.write( "(1) $\"+110+=+s%2At+%2B+%281%2F4%29%2As+\"$
\n" ); document.write( "(1) $\"+110+=+s%2A%28+110+%2F+%28+s%2B4+%29+%29+%2B+%281%2F4%29%2As+\"$
\n" ); document.write( "Multiply both sides by $\"+4%2A%28+s%2B4+%29+\"$
\n" ); document.write( "(1) $\"+440%2A%28+s%2B4+%29+=+440s+%2B+s%2A%28+s%2B4+%29+\"$
\n" ); document.write( "(1) $\"+440s+%2B+1760+=+440s+%2B+s%5E2+%2B+4s+\"$
\n" ); document.write( "(1) $\"+s%5E2+%2B+4s+-+1760+=+0+\"$
\n" ); document.write( "I can complete the square:
\n" ); document.write( "(1) $\"+s%5E2+%2B+4s+%2B+%284%2F2%29%5E2+=+1760+%2B+%284%2F2%29%5E2+\"$
\n" ); document.write( "(1) $\"+s%5E2+%2B+4s+%2B+4+=+1760+%2B+4+\"$
\n" ); document.write( "(1) $\"+s%5E2+%2B+4s+%2B+4+=+1764+\"$
\n" ); document.write( "(1) $\"+%28+s+%2B+2+%29%5E2+=+42%5E2+\"$
\n" ); document.write( "Take the square root of both sides
\n" ); document.write( "(1) $\"+s+%2B+2+=+42+\"$
\n" ); document.write( "(1) $\"+s+=+40+\"$
\n" ); document.write( "and
\n" ); document.write( "(2) $\"+110+=+%28+s+%2B+4+%29%2At+\"$
\n" ); document.write( "(2) $\"+110+=+%28+40+%2B+4+%29%2At+\"$
\n" ); document.write( "(2) $\"+110+=+44t+\"$
\n" ); document.write( "(2) $\"+t+=+2.5+\"$
\n" ); document.write( "and
\n" ); document.write( " $\"+s+%2B+4++=+44+\"$
\n" ); document.write( " $\"+t+%2B+1%2F4+=+2.75+\"$
\n" ); document.write( "-------------------
\n" ); document.write( "Carlos drives 40 mi/hr
\n" ); document.write( "Amy drives 44 mi/hr
\n" ); document.write( "-------------------
\n" ); document.write( "check:
\n" ); document.write( "(1) $\"+110+=+s%2A%28+t+%2B+1%2F4+%29+\"$
\n" ); document.write( "(1) $\"+110+=+40%2A%28+2.5+%2B+1%2F4+%29+\"$
\n" ); document.write( "(1) $\"+110+=+40%2A2.75+\"$
\n" ); document.write( "(1) $\"+110+=+110+\"$
\n" ); document.write( "and
\n" ); document.write( "(2) $\"+110+=+%28+s+%2B+4+%29%2At+\"$
\n" ); document.write( "(2) $\"+110+=+%28+40+%2B+4+%29%2A2.5+\"$
\n" ); document.write( "(2) $\"+110+=+44%2A2.5+\"$
\n" ); document.write( "(2) $\"+110+=+110+\"$
\n" ); document.write( "OK \n" ); document.write( "

\n" );