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
Since Y is 5 ft3/sec lower then Y = 13.5 |