SOLUTION: Ethan is the winner of a 6 mile race and finishes 2 minutes ahead of Ashley. Ethan travels on average 2 mph faster then Ashley. find their average speed. thanks!

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Question 170714: Ethan is the winner of a 6 mile race and finishes 2 minutes ahead of Ashley. Ethan travels on average 2 mph faster then Ashley. find their average speed.
thanks!
Answer by Mathtut(3670) (Show Source):
You can put this solution on YOUR website!
distance equals rate times time. They through a little twist in on this one.... they gave us rate in times of hours and time in terms of minutes...so we will have to adjust one or the other...I will change the time from minutes to hours by dividing by 60. Lets call Ashleys rate r and her time t/60
so Ethans rate will be r+2 and his time will be (t-2)/60
:
6=r(t/60)--->t=360/r
:
6=(r+2)((t-2)/60)--->360=(r+2)((t-2)
:
now lets take t's value from first equation and plug it into second equation.
:
360=(r+2)((360/r)-2)---->360=(r+2)((360-2r)/r)--->360r=(r+2)(360-2r)
:

:
divide by 2
:

since a rate cant be negaive we throw out -20
:
so Ashleys rate is 18--->making Ethans rate 18+2=20--->
there average speed would therefore bemph

Solved by pluggable solver: SOLVE quadratic equation with variable

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=1444 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 18, -20. Here's your graph: