document.write( "Question 167686This question is from textbook ELEMENTARY AND INTERMEDIATE ALGEBRA
\n" ); document.write( ": Brenda and her husband Randy bicycled cross-country
\n" ); document.write( "together. One morning, Brenda rode 30 miles. By traveling
\n" ); document.write( "only 5 miles per hour faster and putting in one more hour,
\n" ); document.write( "Randy covered twice the distance Brenda covered. What
\n" ); document.write( "was the speed of each cyclist? \n" ); document.write( "
Algebra.Com's Answer #123584 by gonzo(654)\"\" \"About 
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i get two possibilities.
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\n" ); document.write( "let t = time
\n" ); document.write( "let r = rate
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\n" ); document.write( "t*r = 30 (equation 1)
\n" ); document.write( "this equation is for brenda.
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\n" ); document.write( "(t+1)*(r+5) = 60 (equation 2)
\n" ); document.write( "this equation is for randy. he rode 1 extra hour and traveled 5 miles per hour faster than brenda.
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\n" ); document.write( "it t*r = 30, then r = 30/t
\n" ); document.write( "substituting 30/t for r in equation 2 gets:
\n" ); document.write( "(t+1)*((30/t)+5) = 60
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\n" ); document.write( "multiply both sides of equation by t:
\n" ); document.write( "t*(t+1)*((30/t)+5) = 60*t
\n" ); document.write( "this is the same as:
\n" ); document.write( "t*((30/t)+5)*(t+1) = 60*t
\n" ); document.write( "this becomes:
\n" ); document.write( "(30+5*t)*(t+1) = 60*t
\n" ); document.write( "this becomes:
\n" ); document.write( "30*t + 30 + 5*t^2 + 5*t = 60*t
\n" ); document.write( "this becomes:
\n" ); document.write( "35*t + 30 + 5*t^2 = 60*t
\n" ); document.write( "subtract 60*t from both sides of equation:
\n" ); document.write( "-25*t + 30 + 5*t^2 = 0
\n" ); document.write( "divide both sides of equation by 5:
\n" ); document.write( "-5*t + 6 + t^2 = 0
\n" ); document.write( "this is the same as:
\n" ); document.write( "t^2 - 5*t + 6 = 0
\n" ); document.write( "factor left side of equation:
\n" ); document.write( "(t-3)*(t+2) = 0
\n" ); document.write( "t = 3
\n" ); document.write( "or
\n" ); document.write( "t = -2
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\n" ); document.write( "since t can't be negative, answer appears to be t = 3.
\n" ); document.write( "if t = 3, then r = 10, since r*3 = 30 becomes r = 10.
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\n" ); document.write( "substituting t = 3 and r = 10 in equation 1:
\n" ); document.write( "r*t=30
\n" ); document.write( "10*3=30
\n" ); document.write( "30=30
\n" ); document.write( "ok
\n" ); document.write( "substituting t = 3 and r = 10 in equation 2:
\n" ); document.write( "(t+1)*(r+5)=60
\n" ); document.write( "(3+1)*(10+5)=60
\n" ); document.write( "(4)*(15)=60
\n" ); document.write( "60=60
\n" ); document.write( "ok
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\n" ); document.write( "answer is:
\n" ); document.write( "t = 3 while r = 10
\n" ); document.write( "Brenda traveled 10 mph for 3 hours to make 30 miles.
\n" ); document.write( "Randy traveled 15 mph for 4 hours to make 60 miles.
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