Question 167686
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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