document.write( "Question 186871: This question is not from a book.
\n" ); document.write( "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 #140084 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let $\"r\"$ = the speed of the vehicle
\n" ); document.write( "Let $\"d\"$ = distance in miles
\n" ); document.write( "Let $\"t\"$ = time in hours
\n" ); document.write( "given:
\n" ); document.write( " $\"d+=+150\"$ mi
\n" ); document.write( " $\"d+=+r%2At\"$
\n" ); document.write( "(1) $\"150+=+r%2At\"$
\n" ); document.write( "(2) $\"150+=+%28r+%2B+20%29%2A%28t+-+2%29\"$
\n" ); document.write( "---------------------------------
\n" ); document.write( "From (1),
\n" ); document.write( " $\"t+=+150%2Fr\"$
\n" ); document.write( "Substitute this in (2)
\n" ); document.write( "(2) $\"150+=+%28r+%2B+20%29%2A%28%28150%2Fr%29+-+2%29\"$
\n" ); document.write( "(2) $\"150+=+150+%2B+3000%2Fr+-+2r+-+40\"$
\n" ); document.write( "Subtract $\"150\"$ from both sides
\n" ); document.write( "(2) $\"0+=+3000%2Fr+-+2r+-+40\"$
\n" ); document.write( "Add $\"40\"$ to both sides
\n" ); document.write( "(2) $\"40+=+3000%2Fr+-+2r\"$
\n" ); document.write( "Multiply both sides by $\"r\"$
\n" ); document.write( "(2) $\"40r+=+3000+-+2r%5E2\"$
\n" ); document.write( "Add $\"2r%5E2\"$ to both sides
\n" ); document.write( "(2) $\"2r%5E2+%2B+40r+=+3000\"$
\n" ); document.write( "divide both sides by $\"2\"$
\n" ); document.write( "(2) $\"r%5E2+%2B+20r+=+1500\"$
\n" ); document.write( "I will find $\"r\"$ by completing the square
\n" ); document.write( "(you could use quadratic formula also)
\n" ); document.write( "(2) $\"r%5E2+%2B+20r++%2B+%2820%2F2%29%5E2+=+1500+%2B+%2820%2F2%29%5E2\"$
\n" ); document.write( "(2) $\"r%5E2+%2B+20r++%2B+100+=+1500+%2B+100\"$
\n" ); document.write( "(2) $\"r%5E2+%2B+20r++%2B+100+=+1600\"$
\n" ); document.write( "Now both sides are perfect squares
\n" ); document.write( "(2) $\"%28r+%2B+10%29%5E2+=+40%5E2\"$
\n" ); document.write( "Take the square roots of both sides
\n" ); document.write( "(2) $\"r+%2B+10+=+40\"$
\n" ); document.write( "(2) $\"r+=+30\"$ (there is a negative solution also, $\"r+=+-50\"$ )
\n" ); document.write( "The speed of his vehicle is 30 mi/hr
\n" ); document.write( "check answer:
\n" ); document.write( "(1) $\"150+=+r%2At\"$
\n" ); document.write( "(1) $\"t+=+150%2F30\"$
\n" ); document.write( "(1) $\"t+=+5\"$ hrs
\n" ); document.write( "and
\n" ); document.write( "(2) $\"150+=+%28r+%2B+20%29%2A%28t+-+2%29\"$
\n" ); document.write( "(2) $\"150+=+%2830+%2B+20%29%2A%285+-+2%29\"$
\n" ); document.write( "(2) $\"150+=+50%2A3\"$
\n" ); document.write( "(2) $\"150+=+150\"$
\n" ); document.write( "OK\r
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