document.write( "Question 654575: a car traveled at 1280 mi at a certain speed. if the speed had been 16mph faster, the trip would have been made in 4hr less time. find the speed. \n" ); document.write( "

Algebra.Com's Answer #408781 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let $\"+s+\"$ = the car's actual speed in mi/hr
\n" ); document.write( "Let $\"+t+\"$ = the car's actual time in hours
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"+1280+=+s%2At+\"$
\n" ); document.write( "(2) $\"+1280+=+%28+s+%2B+16+%29%2A%28+t+-4+%29+\"$
\n" ); document.write( "----------------------------
\n" ); document.write( "(2) $\"+1280+=+s%2At+-+4s+%2B+16t+-+64+\"$
\n" ); document.write( "(2) $\"+1344+=+s%2At+-+4s+%2B+16t+\"$
\n" ); document.write( "Substitute (1) into (2)
\n" ); document.write( "(2) $\"+1344+=+1280+-+4s+%2B+16t+\"$
\n" ); document.write( "(2) $\"+16t+=+4s+%2B+64+\"$
\n" ); document.write( "And, from (1)
\n" ); document.write( "(1) $\"+s+=+1280%2Ft+\"$
\n" ); document.write( "Plug this back into (2)
\n" ); document.write( "(2) $\"+16t+=+4%2A%28+1280%2Ft+%29+%2B+64+\"$
\n" ); document.write( "(2) $\"+16t%5E2+=+5120+%2B+64t+\"$
\n" ); document.write( "(2) $\"+t%5E2+-+4t+-+320+=+0+\"$
\n" ); document.write( "I can solve this by inspection
\n" ); document.write( "(2) $\"+%28+t+-+20+%29%2A%28+t+%2B+16+%29+\"$
\n" ); document.write( " $\"+t+=+20+\"$ ( ignore $\"+t+=+-16+\"$ , can't have negative time )
\n" ); document.write( "Plug this result back into (1)
\n" ); document.write( "(1) $\"+1280+=+s%2A20+\"$
\n" ); document.write( "(1) $\"+s+=+64+\"$
\n" ); document.write( "The car's speed is 64 mi/hr
\n" ); document.write( "check:
\n" ); document.write( "(2) $\"+1280+=+%28+64+%2B+16+%29%2A%28+20+-4+%29+\"$
\n" ); document.write( "(2) $\"+1280+=+80%2A16+\"$
\n" ); document.write( "(2) $\"+1280+=+1280+\"$
\n" ); document.write( "OK
\n" ); document.write( " \n" ); document.write( "

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