SOLUTION: Two rainstorms occured in one week in an are.The 1st storm lasted 25 hours and the second storm lasted 30 hours for a total of 1450ml of rain.What was the rate of rainfall for each

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Question 173366: Two rainstorms occured in one week in an are.The 1st storm lasted 25 hours and the second storm lasted 30 hours for a total of 1450ml of rain.What was the rate of rainfall for each of the two storms if the sum of the two rates were 55 ml per hour?? I have tried multiplying, dividing,and came up with some enormous figure that I know was wrong. Thanks in advance. Judy
Found 3 solutions by jim_thompson5910, scott8148, josmiceli:
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
Let x=rate of first storm (in ml per hour) and y=rate of second storm (in ml per hour)

Since the "sum of the two rates were 55 ml per hour", this means that

Also, if "1st storm lasted 25 hours and the second storm lasted 30 hours for a total of 1450ml of rain", this tells us that

So we have the system of equations:

Let's solve the system by the substitution method.

Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to solve for y.

So let's isolate y in the first equation

Start with the first equation

Subtract from both sides

Rearrange the equation

---------------------

Since , we can now replace each in the second equation with to solve for

Plug in into the second equation. In other words, replace each with . Notice we've eliminated the variables. So we now have a simple equation with one unknown.

Distribute to

Multiply

Combine like terms on the left side

Subtract 1650 from both sides

Combine like terms on the right side

Divide both sides by -5 to isolate x

Divide

-----------------First Answer------------------------------

So the first part of our answer is:

Since we know that we can plug it into the equation (remember we previously solved for in the first equation).

Start with the equation where was previously isolated.

Plug in

Multiply

Combine like terms

-----------------Second Answer------------------------------

So the second part of our answer is:

-----------------Summary------------------------------

So our answers are:

and

So this means that the first storm's rate is 40 ml of water per hour and the second storm's rate is 15 ml of water an hour.

Answer by scott8148(6628)   (Show Source):
You can put this solution on YOUR website!
let x=rate for 1st storm, so 55-x=rate for 2nd storm

25(x) + 30(55-x) = 1450

distributing __ 25x + 1650 - 30x = 1450

subtracting 1650 __ -5x = -200

dividing by -5 __ x=40

substituting __ 55-(40)=15

Answer by josmiceli(19441)   (Show Source):
You can put this solution on YOUR website!
Let = the amount of rain in the 1st storm in ml
Let = the amount of rain in the 2nd storm in ml
The 1st storm lasted 25 hours, so the rate of rainfall was
ml/hr
The second storm lasted 30 hours, so the rate of rainfall was
ml/hr
The sum of the two rates were 55 ml per hour
(1) ml/hr
Also given is the total rainfall of 1450 ml, so
(2) ml
Multiply both sides of (1) by
(1)
(3
Multiply both sides of (2) by
(2)
(4)
Subtract (4) from (3)
ml
And

ml
The two rates of rainfall were

ml/hr
and

ml/hr
The rates of rainfall were 40 ml/hr and 15 ml/hr