SOLUTION: 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 t

Question 171699: 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?
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
for both of them
For Brenda:
(1)
For Randy:
(2)
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Given is:

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Now I can rewrite (1) and (2)
(1)

(2)
(2)
(2)
Multiply both sides by
(2)
(2)
Looking at this, I see and
(2)
This is true if either or
If , then

---------------

---------------
Putting this together,
For Brenda:
(1)
For Randy:
(2)
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These answers work, but what if ?

-----------------

-----------------
Putting these together,
(1)
For Randy:
(2)
These answers work too, so
The speeds of the cyclists were either
(1) Brenda went 10 mi/hr and Randy went 15 mi/hr
(2) Brenda went 15 mi/hr and Randy went 20 mi/hr
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