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 co

Algebra ->  Polynomials-and-rational-expressions -> 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 co      Log On


   

Question 167686This question is from textbook ELEMENTARY AND INTERMEDIATE ALGEBRA
: 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 ALGEBRA

Found 2 solutions by ankor@dixie-net.com, gonzo:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
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
:
B traveled 30 mi
R traveled 60 mi (twice B's distance)
:
Write a time equation: Time = distance%2Fspeed
:
B's time + 1 hr = R's time
30%2Fs + 1 = 60%2F%28%28s%2B5%29%29
Multiply equation by s(s+5); results:
30(s+5) + s(s+5) = 60s
:
30s + 150 + s^2 + 5s - 60s = 0
:
s^2 - 25s + 150 = 0; our old friend, the quadratic equation!
Factor:
(s - 15))(x - 10) = 0
:
both solutions will work:
s = 10 mph is B's speed, obviously, 15 mph = R's speed
and
s = 15 mph is B's speed, then 20 mph = R's speed
:
:
Check both solutions in the time equation
30%2F10 + 1 = 60%2F15
and
30%2F15 + 1 = 60%2F20

Answer by gonzo(654) About Me  (Show Source):
You can put this solution on YOUR website!
i get two possibilities.
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let t = time
let r = rate
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t*r = 30 (equation 1)
this equation is for brenda.
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(t+1)*(r+5) = 60 (equation 2)
this equation is for randy. he rode 1 extra hour and traveled 5 miles per hour faster than brenda.
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it t*r = 30, then r = 30/t
substituting 30/t for r in equation 2 gets:
(t+1)*((30/t)+5) = 60
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multiply both sides of equation by t:
t*(t+1)*((30/t)+5) = 60*t
this is the same as:
t*((30/t)+5)*(t+1) = 60*t
this becomes:
(30+5*t)*(t+1) = 60*t
this becomes:
30*t + 30 + 5*t^2 + 5*t = 60*t
this becomes:
35*t + 30 + 5*t^2 = 60*t
subtract 60*t from both sides of equation:
-25*t + 30 + 5*t^2 = 0
divide both sides of equation by 5:
-5*t + 6 + t^2 = 0
this is the same as:
t^2 - 5*t + 6 = 0
factor left side of equation:
(t-3)*(t+2) = 0
t = 3
or
t = -2
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since t can't be negative, answer appears to be t = 3.
if t = 3, then r = 10, since r*3 = 30 becomes r = 10.
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substituting t = 3 and r = 10 in equation 1:
r*t=30
10*3=30
30=30
ok
substituting t = 3 and r = 10 in equation 2:
(t+1)*(r+5)=60
(3+1)*(10+5)=60
(4)*(15)=60
60=60
ok
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answer is:
t = 3 while r = 10
Brenda traveled 10 mph for 3 hours to make 30 miles.
Randy traveled 15 mph for 4 hours to make 60 miles.
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