SOLUTION: A trip involves 15 miles on a dirt trail and 90 miles on a freeway. The velocity for the freeway portion was 30 mph more than the velocity for the dirt trail portion. The entire tr

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Question 514833: A trip involves 15 miles on a dirt trail and 90 miles on a freeway. The velocity for the freeway portion was 30 mph more than the velocity for the dirt trail portion. The entire trip took 2 hours. What was the velocity, in miles per hour, for each part of the trip?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A trip involves 15 miles on a dirt trail and 90 miles on a freeway.
The velocity for the freeway portion was 30 mph more than the velocity for the dirt trail portion.
The entire trip took 2 hours.
What was the velocity, in miles per hour, for each part of the trip?
:
Let s = speed on dirt
then
(s+30) = speed on freeway
:
Write a time equation; time = dist/speed
:
dirt time + freeway time = 2 hrs
15%2Fs + 90%2F%28%28s%2B30%29%29 = 2
multiply by s(s+30), results:
15(s+30) + 90s = 2s(s+30)
15s + 450 + 90s = 2s^2 + 60s
105s + 450 = 2s^2 + 60s
0 = 2s^2 + 60s - 105s - 450
A quadratic equation
2s^2 - 45s - 450 = 0
Factors to:
(2s + 15)(s - 30) = 0
The positive solution
s = 30 mph on dirt
then
30+30 = 60 mph on the freeway
:
:
You can check this by finding the actual time at each speed