SOLUTION: A car travels 380 miles averaging a certain speed. If the car had gone 5 mph faster the trip would have take 1 hour less. What was the average speed?

Question 1005932: A car travels 380 miles averaging a certain speed. If the car had gone 5 mph faster the trip would have take 1 hour less. What was the average speed?
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
A car travels 380 miles averaging a certain speed. If the car had gone 5 mph faster the trip would have take 1 hour less. What was the average speed?
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d = r*t
t = d/r
t = 380/r
t-1 = 380/(r+5)
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380/r - 1 = 380/(r+5)
(380 - r)/r = 380/(r+5)
(380 - r)*(r+5) = 380r
(r-380)*(r+5) = -380r
r^2 + 5r - 1900 = 0

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=7625 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 41.1606229914325, -46.1606229914325. Here's your graph:

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r =~ 41.16 mi/hr (Ignore the negative value)

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