document.write( "Question 228093: Brenda and her husband Randy bicycled cross-country together. One morning, Brenda rode 30 miles. By traveling only 5 miles per hour faster and putting in one more hour, Randy covered twice the distance Brenda covered. What was the speed of each cyclist? \n" ); document.write( "
Algebra.Com's Answer #169488 by ankor@dixie-net.com(22740)\"\" \"About 
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Brenda and her husband Randy bicycled cross-country together.
\n" ); document.write( " One morning, Brenda rode 30 miles.
\n" ); document.write( " By traveling only 5 miles per hour faster and putting in one more hour,
\n" ); document.write( "Randy covered twice the distance Brenda covered.
\n" ); document.write( " What was the speed of each cyclist?
\n" ); document.write( ":
\n" ); document.write( "Let s = B's speed
\n" ); document.write( "then
\n" ); document.write( "(s+5) = R's speed
\n" ); document.write( ":
\n" ); document.write( "Write a time equation Time = dist/speed
\n" ); document.write( "B's time + 1 hr = R's time
\n" ); document.write( "\"30%2Fs\" + 1 = \"60%2F%28s%2B5%29\"
\n" ); document.write( "Multiply equation by s(s+5), results
\n" ); document.write( "30(s+5) + s(s+5) = 60s
\n" ); document.write( ":
\n" ); document.write( "30s + 150 + s^2 + 5s = 60s
\n" ); document.write( ":
\n" ); document.write( "Group like terms on the left
\n" ); document.write( "s^2 + 30s + 5s - 60s + 150 = 0
\n" ); document.write( ":
\n" ); document.write( "A quadratic equation
\n" ); document.write( "s^2 - 25s + 150 = 0
\n" ); document.write( ":
\n" ); document.write( "Factors to
\n" ); document.write( "(s - 15)(s - 10) = 0
\n" ); document.write( ":
\n" ); document.write( "Two solutions
\n" ); document.write( "s = 10 mph
\n" ); document.write( "s = 15 mph
\n" ); document.write( ";
\n" ); document.write( ":
\n" ); document.write( "Check both these solutions in the original equation, both will work \n" ); document.write( "
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