SOLUTION: On a recent trip, Sarah's car traveled 20 mph faster on the first 120 miles than it did on the remaining 80 miles. The total time for the trip was 4 hr. Find the speed of Sarah's

Question 712954: On a recent trip, Sarah's car traveled 20 mph faster on the first 120 miles than it did on the remaining 80 miles. The total time for the trip was 4 hr. Find the speed of Sarah's car on the first part of the trip. I used the distance = rate * time.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
On a recent trip, Sarah's car traveled 20 mph faster on the first 120 miles than it did on the remaining 80 miles. The total time for the trip was 4 hr. Find the speed of Sarah's car on the first part of the trip.
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1st leg of trip DATA:
distance = 120 miles ; rate = x+20 mph ; time = d/r = 120/(x+20) hrs
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2nd leg of the trip DATA:
distance = 80 miles ; rate = x mph ; time = d/r = 80/x hrs
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Equation:
time + time = 4 hrs
120/(x+20) + 80/x = 4
---
30/(x+20) + 20/x = 1
30x + 20(x+20) = x(x+20)
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30x + 20x + 400 = x^2 + 20x
----
x^2 -30x -400 = 0
----
x^2-40x+10x-400 = 0
x(x-40)+10(x-40) = 0
(x-40)(x+10) = 9
Positive solution:
x = 40 mph (rate on leg 2 of the trip)
x+20 = 60 mph (rate on leg 1 of the trip)
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Cheers,
Stan H.
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