SOLUTION: Brenda and Randy bicycling across country. Brenda rode 30miles. Traveling 5 miles per hour faster and putting in one hour more, Randy covered twice the distance of Brenda. What is

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Question 324236: Brenda and Randy bicycling across country. Brenda rode 30miles. Traveling 5 miles per hour faster and putting in one hour more, Randy covered twice the distance of Brenda. What is the speed of each cyclist.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Rate*Time=Distance
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Let Rb=Brenda's rate (speed) and Rr=Randy's rate.
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Rb%2AT=30
T=30%2FRb
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Rr%2A%28T%2B1%29=60
Rr=Rb%2B5
%28Rb%2B5%29%28T%2B1%29=60
Substituting,
%28Rb%2B5%29%2830%2FRb%2BRb%2FRb%29=60
%28Rb%2B5%29%2830%2BRb%29=60Rb
30Rb%2BRb%5E2%2B150%2B5Rb=60Rb
Rb%5E2-25Rb%2B150=0
%28Rb-10%29%28Rb-15%29=0
Two solutions:
Rb-10=0
Rb=10mph
So then,
Rr=15mph
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Rb-15=0
Rb=15mph
So then,
Rr=20mph