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 cov

Question 414433: 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 stanbon(75887) (Show Source): You can put this solution on YOUR website!
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.
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Brenda DATA:
distance = 30 miles ; rate = x mph ; time = 30/x hrs
---------
New DATA
Randy DATA:
distance = 60 miles ; rate = (x+5) mph ; time = 60/(x+5) hrs
----
Equation:
Brenda time - Randy time = 1 hr.
30/x - 60/(x+5) = 1
----
30(x+5) - 60x = x(x+5)
30x+150 - 60x = x^2+5x
---
x^2+35x-150 = 0
Use the Quadratic Formula to get x = 3.86 mph (Brenda's rate)
x+5 = 8.86 mph (Randy's rate)
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Cheers,
Stan H.
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