Math Mamas- Help me set up this problem?

[MamaSprout]

Dolciani (with a side of Alcumus) has turned out to be our Goldilocks book for Algebra. I haven't tracked down a reasonably-priced solutions manual yet (1988 Structure and Method), but we haven't needed one so far.

 

However, I'm having a high school algebra memory lapse for this one:

 

An 800 liter tank is half full of water and is being filled with water pumped at the rate of 45 liters per minute from a full 940 liter tank. How long will it take before the the two tanks contain the same amount of water?

 

I know the answer is 6 minutes, but I'm not sure how to set this up algebraically.

 

Can anyone help me set this up? I know it should be simple. :001_rolleyes:

 

TIA!

Edited May 9, 2016 by elladarcy

[Carpe]

800+45n=940-45n

Where n is the time in minutes

Maybe? I need to start brushing up on my algebra, it's coming up way too quickly.

[Cosmos]

Dolciani (with a side of Alcumus) has turned out to be our Goldilocks book for Algebra. I haven't tracked down a reasonably-priced solutions manual yet (1988 Structure and Method), but we haven't needed one so far.

 

However, I'm having a high school algebra memory lapse for this one:

 

An 800 liter tank is half full of water and is being filled with water pumped at the rate of 45 liters per minute from a full 940 liter tank. How long will it take before the the two tanks contain the same amount of water?

 

I know the answer is 6 minutes, but I'm not sure how to set this up algebraically.

 

Can anyone help me set this up? I know it should be simple. :001_rolleyes:

 

TIA!

 

Let t measure the time in minutes.

 

The first tank begins half full (400L) and adds 45L per minute. Call its volume A.

 

A = 400 + 45t

 

The second tank begins full (940L) and loses 45L per minute. Call its volume B.

 

B = 940 - 45t

 

When will they contain the same amount of water? That's when A = B.

 

400 + 45t = 940 - 45t

 

90t = 540

 

t = 6

 

******

 

Alternatively, consider that altogether the tanks have 1340L of water to begin. They will be equal when they each have 670L. That means tank A must gain 270L and tank B must lose 270L. Since the water flows at 45L per minute, this will take 270/45 = 6 minutes.

 

 

[Carpe]

800+45n=940-45n

Where n is the time in minutes

Maybe? I need to start brushing up on my algebra, it's coming up way too quickly.

Nope. I totally misread that.

(1/2)×800 +45n = 940-45n ?

My kids are doomed lol

[MamaSprout]

Awesome, thanks! I see my error now, and it was a silly one. I could get the answer figuring it by the "alternative" method.... but as it Algebra, I thought maybe I should set it up algebraically. :o)

 

Hooray for the hive!

 

Thanks again.

[letsplaymath]

Mental math method: The tanks differ by 940 - 400 = 540 liters of water. Every minute, the fuller tank loses 45 and the emptier tank gains 45, so they move closer together at 90 liters/minute. They will be even in 540/90 = 6 mins.

 

Not what the algebra book wants you to do, but it makes a good common-sense check.