document.write( "Question 6024: Ruth bicycles 5km/h slower than bill. In the time that it takes Ruth to bicycle 42km, bill can bicycle 57km. How fast does each bicyclist travel? \n" ); document.write( "

Algebra.Com's Answer #3165 by Abbey(339) $\"\"$ $\"About$

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let bill's rate = x
\n" ); document.write( "let ruth's rate = x-5
\n" ); document.write( "bill's distance is 57 km
\n" ); document.write( "ruth's distance is 42 km
\n" ); document.write( "both times are the same, so use time=distance/rate and set the equations equal to one another
\n" ); document.write( "bill's equation:
\n" ); document.write( "time=57/x
\n" ); document.write( "ruth's equation:
\n" ); document.write( "time = 42/x-5
\n" ); document.write( " $\"57%2Fx=42%2F%28x-5%29\"$
\n" ); document.write( "multiply by x(x-5) to clear the denominators:
\n" ); document.write( " $\"57x-285=42x\"$
\n" ); document.write( "add 285 to both sides:
\n" ); document.write( " $\"57x=42x%2B285\"$
\n" ); document.write( "subtract 42x from both sides:
\n" ); document.write( " $\"15x=285\"$
\n" ); document.write( "divide both sides by 15:
\n" ); document.write( " $\"x=15\"$ so bill's rate is 19 kmh
\n" ); document.write( "and ruth's is 5 kmh slower, or 14kmh\r
\n" ); document.write( "\n" ); document.write( "check it to see:
\n" ); document.write( "57/19 = 3 hours
\n" ); document.write( "42/14= 3 hours
\n" ); document.write( " \n" ); document.write( "

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