document.write( "Question 179409: Steve traveled 150 miles at a certain speed. Had he gone 20mph faster, the trip would have taken 2 hours less. Find the speed of his vehicle. \n" ); document.write( "

Algebra.Com's Answer #134378 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
(1) $\"150+=+r%2At\"$
\n" ); document.write( "(2) $\"150+=+%28r+%2B+20%29%2A%28t+-+2%29\"$
\n" ); document.write( "Subtract (1) from (2)
\n" ); document.write( " $\"0+=+%28r+%2B+20%29%28t+-+2%29+-+r%2At\"$
\n" ); document.write( " $\"r%2At+=+r%2At+%2B+20t+-+2r+-+40\"$
\n" ); document.write( " $\"2r+=+20t+-+40\"$
\n" ); document.write( "And, since
\n" ); document.write( " $\"150+=+r%2At\"$
\n" ); document.write( " $\"t+=+150%2Fr\"$
\n" ); document.write( " $\"2r+=+20%2A%28150%2Fr%29+-+40\"$
\n" ); document.write( " $\"2r%5E2+=+3000+-+40r\"$
\n" ); document.write( " $\"2r%5E2+%2B+40r+-+3000+=+0\"$
\n" ); document.write( " $\"r%5E2+%2B+20r+-+1500+=+0\"$
\n" ); document.write( "Solve by completing the square
\n" ); document.write( " $\"r%5E2+%2B+20r+%2B+%2820%2F2%29%5E2+=+1500+%2B+%2820%2F2%29%5E2\"$
\n" ); document.write( "Notice the left side is a perfect square
\n" ); document.write( "And so is the right side
\n" ); document.write( " $\"%28r+%2B+10%29%5E2+=+1600\"$
\n" ); document.write( "Take the square root of both sides
\n" ); document.write( " $\"r+%2B+10+=+40\"$
\n" ); document.write( " $\"r+=+30\"$
\n" ); document.write( "The speed is 30 mi/hr
\n" ); document.write( " check:
\n" ); document.write( "(1) $\"150+=+30%2At\"$
\n" ); document.write( " $\"t+=+5\"$ hrs
\n" ); document.write( "(2) $\"150+=+%28r+%2B+20%29%2A%28t+-+2%29\"$
\n" ); document.write( "(2) $\"150+=+%2830+%2B+20%29%2A%28t+-+2%29\"$
\n" ); document.write( "(2) $\"150+=+50%2A%28t+-+2%29\"$
\n" ); document.write( " $\"3+=+t+-+2\"$
\n" ); document.write( " $\"t+=+5\"$ hrs
\n" ); document.write( "OK \n" ); document.write( "

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