SOLUTION: I need help with this Amy travels 450 miles at certain speed. If the car had gone 15 mph faster, the trip would have taken 1 hour less. I need to find amy's speed.

Algebra ->  Linear-equations -> SOLUTION: I need help with this Amy travels 450 miles at certain speed. If the car had gone 15 mph faster, the trip would have taken 1 hour less. I need to find amy's speed.      Log On


   

Question 120930: I need help with this
Amy travels 450 miles at certain speed. If the car had gone 15 mph faster, the trip would have taken 1 hour less. I need to find amy's speed.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Amy travels 450 miles at certain speed. If the car had gone 15 mph faster, the trip would have taken 1 hour less. I need to find Amy's speed.
:
Let s = the "certain speed"
Then
(s+15) = "If" speed
:
Write a time equation: Time = Distance/speed
:
"Certain speed" time - 1 hr = "If" speed time
450%2Fs - 1 = 450%2F%28%28s%2B15%29%29
:
Multiply equation by s(s+15) to get rid of the denominators
:
s(s+15)*450%2Fs - s(s+15)(1) = s(s+15)*450%2F%28%28s%2B15%29%29
:
Cancel out the denominators and you have:
450(s+15) - (s^2 + 15s) = 450s
:
450s + 6750 - s^2 - 15s = 450s
:
-s^2 - 15s +450s - 450s + 6750 = 0; arrange as a quadratic equation
:
-s^2 - 15s + 6750 = 0
:
s^2 + 15s - 6750 = 0; multiplied by -1 (easier to factor)
:
Factors to
(s+90)(s-75) = 0
Positive solution:
s = +75 mph is Amy's speed
:
:
Check solution by finding the time for each scenario
450/75 = 6 hrs
450/90 = 5 hrs
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differs 1 hr; confirms our solution