document.write( "Question 953754: A track and field runner saves 1 hour by covering 112 km at a rate which is 2 km per hour faster than usual rate. How many hours does he usually take to travel this distance? \n" ); document.write( "

Algebra.Com's Answer #582565 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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A track and field runner saves 1 hour by covering 112 km at a rate which is 2 km per hour faster than usual rate.
\n" ); document.write( " How many hours does he usually take to travel this distance?
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\n" ); document.write( "let s = his normal running speed
\n" ); document.write( "then
\n" ); document.write( "(s+2) = his faster running speed
\n" ); document.write( ":
\n" ); document.write( "Write a time equation; time = dist/speed
\n" ); document.write( "normal time - faster time = 1 hr
\n" ); document.write( " $\"112%2Fs\"$ - $\"112%2F%28%28s%2B2%29%29\"$ = 1
\n" ); document.write( "multiply equation by s(s+2)
\n" ); document.write( "s(s+2)* $\"112%2Fs\"$ - s(s+2)* $\"112%2F%28%28s%2B2%29%29\"$ = 1s(s+2)
\n" ); document.write( "Cancel the denominators
\n" ); document.write( "112(s+2) - 112s = s^2 + 2s
\n" ); document.write( "112s + 224 - 112s = s^2 + 2s
\n" ); document.write( "combine like terms on the right to form a quadratic equation
\n" ); document.write( "0 = s^2 + 2s - 224
\n" ); document.write( "factors to
\n" ); document.write( "(s+16)(s-14) = 0
\n" ); document.write( "The positive solution
\n" ); document.write( "s = 14 km/hr is the normal speed
\n" ); document.write( "find the normal time
\n" ); document.write( "112/14 = 8 hrs is the normal time
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Confirm this by finding the time at the faster speed
\n" ); document.write( "112/16 = 7 hrs, 1 hr less
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