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 cover

Algebra ->  Rate-of-work-word-problems -> 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 cover      Log On


   

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?
Answer by ankor@dixie-net.com(22740) About Me  (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?
:
Let s = B's speed
then
(s+5) = R's speed
:
Write a time equation Time = dist/speed
B's time + 1 hr = R's time
30%2Fs + 1 = 60%2F%28s%2B5%29
Multiply equation by s(s+5), results
30(s+5) + s(s+5) = 60s
:
30s + 150 + s^2 + 5s = 60s
:
Group like terms on the left
s^2 + 30s + 5s - 60s + 150 = 0
:
A quadratic equation
s^2 - 25s + 150 = 0
:
Factors to
(s - 15)(s - 10) = 0
:
Two solutions
s = 10 mph
s = 15 mph
;
:
Check both these solutions in the original equation, both will work