document.write( "Question 435264: In one hour, Ed drives 25 miles farther in his car than Frank can cycle on his bike. If it takes Frank 1 1/2 hours longer to cycle 75 miles than it take Ed in his car, how fast can Frank cycle?\r
\n" ); document.write( "\n" ); document.write( "Please help me with this problem, thanks. \n" ); document.write( "

Algebra.Com's Answer #301299 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
The 1st sentence says that Ed's speed is 25 miles/hr
\n" ); document.write( "faster than Frank's
\n" ); document.write( "Let $\"s\"$ = Frank's speed
\n" ); document.write( "Let $\"t\"$ = Ed's time to go 75 miles in his car
\n" ); document.write( "Frank's equation:
\n" ); document.write( " $\"+75+=+s%2A%28t+%2B+1.5%29+\"$
\n" ); document.write( "Ed's equation:
\n" ); document.write( " $\"+75+=+%28s+%2B+25%29%2At+\"$
\n" ); document.write( "-------------------------
\n" ); document.write( "This is 2 equations with 2 uhnknowns,
\n" ); document.write( "so it's solvable
\n" ); document.write( "Since the distances are equal,
\n" ); document.write( " $\"+s%2A%28t+%2B+1.5%29+=+%28s+%2B+25%29%2At+\"$
\n" ); document.write( " $\"+s%2At+%2B+1.5s+=+s%2At+%2B+25t+\"$
\n" ); document.write( " $\"+1.5s+=+25t+\"$
\n" ); document.write( " $\"+t+=+.06s+\"$
\n" ); document.write( " $\"+75+=+s%2A%28.06s+%2B+1.5%29+\"$
\n" ); document.write( " $\"+75+=+.06s%5E2+%2B+1.5s+\"$
\n" ); document.write( " $\"+6s%5E2+%2B+150s+-+7500+=+0+\"$
\n" ); document.write( " $\"+2s%5E2+%2B+50s+-+2500+=+0+\"$
\n" ); document.write( "Using 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( " $\"a+=+2\"$
\n" ); document.write( " $\"b+=+50\"$
\n" ); document.write( " $\"c+=+-2500\"$
\n" ); document.write( " $\"s+=+%28-50+%2B-+sqrt%28+50%5E2-4%2A2%2A%28-2500%29+%29%29%2F%282%2A2%29+\"$
\n" ); document.write( " $\"s+=+%28-50+%2B-+sqrt%28+2500+%2B+20000+%29%29+%2F+4+\"$
\n" ); document.write( " $\"+s+=+%28+-50+%2B+150+%29%2F4+\"$
\n" ); document.write( " $\"+s+=+100%2F4+\"$
\n" ); document.write( " $\"+s+=+25+\"$
\n" ); document.write( "Frank's speed is 25 mi/hr
\n" ); document.write( "check answer:
\n" ); document.write( " $\"+75+=+s%2A%28t+%2B+1.5%29+\"$
\n" ); document.write( " $\"+75+=+25%2A%28t+%2B+1.5%29+\"$
\n" ); document.write( " $\"+75+=+25t+%2B+37.5+\"$
\n" ); document.write( " $\"+25t+=+37.5+\"$
\n" ); document.write( " $\"+t+=+1.5+\"$ hr
\n" ); document.write( "OK
\n" ); document.write( " $\"+75+=+%28s+%2B+25%29%2At+\"$
\n" ); document.write( " $\"+75+=+%2825+%2B+25%29%2At+\"$
\n" ); document.write( " $\"+75+=+50t+\"$
\n" ); document.write( " $\"+t+=+1.5+\"$
\n" ); document.write( "OK\r
\n" ); document.write( "
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