SOLUTION: #13. A car traveling east at 45 miles per hour passes a certain intersection at 3 pm. Another car traveling north at 60 miles per hour passes the same intersection 25 minutes lat

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Question 146811: #13. A car traveling east at 45 miles per hour passes a certain intersection at 3 pm. Another car traveling north at 60 miles per hour passes the same intersection 25 minutes later. To the nearest minute, figure out when the cars are exactly 40 miles apart.
Answer by edjones(8007) (Show Source):
You can put this solution on YOUR website!
When the 2nd car reaches the intersection the 1st car is 45*25/60=18.75 miles east of it.
We have a right triangle with the hypotenuse=40
d=st d=distance s=speed, t=time
Let a=60t
b=45t+18.75, c=40
a^2+b^2=c^2
60t^2+(45t+18.75)^2=40^2
3600t^2+2025t^2+1687.5t+351.56=1600
5625t^2+1687.5t-1248.44=0
t=.344414 hr
=21 min (approx)
.
Ed
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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=30937556.25 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 0.344413681939415, -0.644413681939415. Here's your graph: