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

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Question 192127: 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 bike speed
then
(s+5) = R's speed
:
From the information given:
B traveled 30 mi
R traveled 60 mi
:
Write a time equation; Time = dist%2Fspeed
:
B's time + 1 hr = R's time
30%2Fs + 1 = 60%2F%28%28s%2B5%29%29
Multiply by s(s+5)
s(s+5)*30%2Fs + 1*s(s+5) = s(s+5)*60%2F%28%28s%2B5%29%29
Cancel the denominators, leaving
30(s+5) + s(s+5) = 60s
:
30s + 150 + s^2 + 5s - 60s = 0
:
Combine as a quadratic equation:
s^2 - 25s + 150 = 0
Factors to:
(x-10)(x-15) = 0
Two good solutions for B's speed
s = 10 mph
s = 15 mph
:
Check solution; B's speed =10, R's speed = 15
30%2F10 + 1 = 60%2F15
3 + 1 = 4
:
Check solution; B's speed =15, R's speed = 20
30%2F15 + 1 = 60%2F20
2 + 1 = 3
:
:
Did this make sense to you? Any questions?