# Thread: Factoring response time equation

1. ## Factoring response time equation

Remember the calculation of response time in the lecture?

R = SQ + S(2)

Based on one Queuing Theorem:

Q = a * R(3)

Manipulating equations (2) and (3) using Factoring method, we obtain:

S
R = ---------- (4)
1 – a S

Show how you manipulate the two equations (2) and (3) in order to get (4).

The lecture notes remind us that Q=a(SQ=S) if that helps anyone out there. Thanks so much!

2. Originally Posted by Heather
Remember the calculation of response time in the lecture?

R = SQ + S(2)

Based on one Queuing Theorem:

Q = a * R(3)

Manipulating equations (2) and (3) using Factoring method, we obtain:

S
R = ---------- (4)
1 – a S

Show how you manipulate the two equations (2) and (3) in order to get (4).

The lecture notes remind us that Q=a(SQ=S) if that helps anyone out there. Thanks so much!
I doubt most of us are taking this class with you!

Can you give us some background in regard to what you are talking about?

-Dan

3. Most of what we are studying right now is factoring and finding GCF. Somehow with this problem you are supposed to be doing factoring, but the only way i see it possible is by starting with substitution.

4. Originally Posted by Heather
Remember the calculation of response time in the lecture?

R = SQ + S(2)

Based on one Queuing Theorem:

Q = a * R(3)

Manipulating equations (2) and (3) using Factoring method, we obtain:

S
R = ---------- (4)
1 – a S

Show how you manipulate the two equations (2) and (3) in order to get (4).

The lecture notes remind us that Q=a(SQ=S) if that helps anyone out there. Thanks so much!
Oh okay, from the way you phrased the question I thought there was more to it.

So we have:
$R = SQ + S$

and

$Q = aR$

So put the bottom equation into the top:
$R = S(aR) + S = aSR + R$

Now we want to solve for R:
$R - aSR = S$

There is a common R to both terms on the left, so factor it:
$(1 - aS)R = S$

Now divide:
$R = \frac{S}{1 - aS}$

-Dan

5. Thank you soooooo much this has been driving me crazy! But now i feel dumb because this was very simple

6. Originally Posted by Heather
Thank you soooooo much this has been driving me crazy! But now i feel dumb because this was very simple
Don't feel dumb. There have been times I've forgotten how to add. (Seriously!) Everyone has their moments.

-Dan