Solve the Following:

Two streams have a combined flow rate of 32.4 cubic feet per second. We know that one stream has a flow rate that is 5 cubic feet per second higher than the other. What is the flow rate of the two streams?

Solution 1:
If we assume x is equal to the flow rate of the slower stream than the flow rate of the faster stream will be equal to

(x + 5) ft³/sec

We also know that together the two streams will release the following:

x + (x +5) = 32

So we get:
2x + 5 = 32

2x = 27
x = 13.5

When we solve for x we get a flow rate of 13.5 ft³/sec and since we know that the second stream has a flow rate which is 5 ft³/sec faster we can add 5 to the first flow rate of 13.5 to get 18.5 ft³/sec.

Now let’s check our work. If we add together the tow flow rate we should get a combined flow of 32 ft³/sec. Since 13.5 + 18.5 add up to 32 we know we have done this problem correctly.

Solution 2:
We could have also solved this equation by solving simultaneous equations. I will now show you how to do this using the same example.

Lets start by assuming that X is equal to the larger flow rate and Y is equal to the smaller flow rate.

We there for know that X + Y = 32 and X – Y = 5

Now let’s set up our equations like this:

X + Y = 32
X – Y = 5

If we simplify these two equations we see that we get:

2X = 37

And

X = 18.5