SOLUTION: 20.) 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. Rand

Algebra ->  Test -> SOLUTION: 20.) 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. Rand      Log On


   

Question 164004This question is from textbook Elementary and Intermediate
: 20.) 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? This question is from textbook Elementary and Intermediate

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, distance 30 mi
then
(s+5) = R's speed, distance 60 mi
:
Write a time equation: Time = distance/speed
:
B's time + 1 hr = R's time
30%2Fs + 1 = 60%2F%28%28s%2B5%29%29
Multiply equation by s(s+5)
30(s+5) + s(s+5) = 60s
:
30s + 150 + s^2 + 5s = 60s
:
Arrange as a quadratic equation:
s^2 + 5s + 30s - 60s + 150 = 0
:
s^2 - 25s + 150 = 0
Factors to:
(s - 10)(s - 15) = 0
:
s = 10 mph is B's speed, then R's speed = 15 mph
or
s = 15 mph is B's speed, then R's speed = 20 mph
:
If substitute either value for s you will find that it's true