SOLUTION: Joe and Nancy decide to take a road trip. The first 120 miles of the drive is pretty​ easy, while the last 84 miles of the drive is filled with curves. They drove at an avera

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Question 1087754: Joe and Nancy decide to take a road trip. The first 120 miles of the drive is pretty​ easy, while the last 84 miles of the drive is filled with curves. They drove at an average of 9 miles per hour faster for the first 120 miles of the trip. The entire trip took 3 hours. How fast were Joe and Nancy driving for the first 120 miles of the​ trip?
Found 2 solutions by rothauserc, MathTherapy:
Answer by rothauserc(4718)   (Show Source): You can put this solution on YOUR website!
let r be the rate for the slower, 84 miles, portion of the trip
let t1 be the time for the 120 miles portion of the trip and t2 for the 84 miles portion
:
1) t1 + t2 = 3
2) (r+9)*t1 = 120 and r*t2 = 84
3) (r+9)*t1 + r*t2 = 120 + 84 = 204
:
expand the left side of equation 3
:
r*t1 + 9*t1 + r*t2 = 204
r*(t1+t2) +9*t1 = 204
:
substitute for (t1+t2) by using equation 1)
:
3*r + 9*t1 = 204
:
divide both sides of = by 3
:
4) r + 3*t1 = 68
:
use the equation for t1 from the equations defined at 2)
:
t1 = 120 / (r+9)
:
substitute for t1 in equation 4)
:
r + 3*(120/(r+9)) = 68
:
r^2 +9r +360 = 68 * (r+9)
:
r^2 -59r -252 = 0
:
(r-63)*(r+4) = 0
:
r = 63 and r = -4
:
we reject the negative value for r
:
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Joe and Nancy drove 63+9 = 72 miles per hour for the first 120 miles of the​ trip
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:
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
Joe and Nancy decide to take a road trip. The first 120 miles of the drive is pretty​ easy, while the last 84 miles of the drive is filled with curves. They drove at an average of 9 miles per hour faster for the first 120 miles of the trip. The entire trip took 3 hours. How fast were Joe and Nancy driving for the first 120 miles of the​ trip?
Let speed during the 120-mile trip be S

Then speed during the 84-mile trip = S – 9

We then get the following TIME equation: 

120(S – 9) + 84S = 3S(S – 9) -------- Multiplying by LCD, S(S – 9)











(S - 72)(S - 5) = 0

S - 72 = 0               OR               S - 5 = 0

S, or 	         OR	      S = 5 (ignore) 

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