document.write( "Question 949051: A car traveled 960 miles at a certain speed. If the speed had been 12 mph faster, the trip could have been made in 4 hours less time. Find the speed. \n" ); document.write( "

Algebra.Com's Answer #579335 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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A car traveled 960 miles at a certain speed.
\n" ); document.write( " If the speed had been 12 mph faster, the trip could have been made in 4 hours less time.
\n" ); document.write( " Find the speed.
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\n" ); document.write( "Let s = the speed
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\n" ); document.write( "Write a time equation; time = dist/speed
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\n" ); document.write( "normal time - faster time = 4 hrs
\n" ); document.write( " $\"960%2Fs\"$ - $\"960%2F%28%28s%2B12%29%29\"$ = 4
\n" ); document.write( "multiply equation by s(s+12)
\n" ); document.write( "960(s+12) - 960s = 4s(s+12)
\n" ); document.write( "960s + 11520 - 960s = 4s^2 + 48s
\n" ); document.write( "Combine to form a quadratic equation on the right
\n" ); document.write( "0 = 4s^2 + 48s - 11520
\n" ); document.write( "simplify, divide by 4
\n" ); document.write( "s^2 + 12s - 2880 = 0
\n" ); document.write( "You can use the quadratic formula; a=1; b=12; c=-2880, but this will factor
\n" ); document.write( "(s+60)(s-48) = 0
\n" ); document.write( "The positive solution is all we want here
\n" ); document.write( "s = 48 mph is the speed of the car
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\n" ); document.write( "Check this, find the times at each speed
\n" ); document.write( "960/48 = 20 hrs
\n" ); document.write( "960/60 = 16 hrs
\n" ); document.write( "---------------
\n" ); document.write( "differ by: 4 hrs \n" ); document.write( "

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