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# When Blanca puts the stopper in place and the faucet running, the bathtub can be filled in 16 minuets. When she turns the faucet off and rem

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When Blanca puts the stopper in place and the faucet running, the bathtub can be filled in 16 minuets. When she turns the faucet off and removes, the tub will empty in 20 minuets. If Blanca turns the faucet on and does not put the stopper in place, how long will it take her to fill the tub?

It needs an equation to find the answer

Guest Apr 27, 2015

#3
+17745
+10

Since the bathtub can be filled in 16 minutes, the rate is 1 bathtub / 16 minutes  or  1/16.

Since the bathtub can be emptied in 20 minutes, the rate is -1 bathtub / 20 minutes  or  -1/20.

Let  n  be the number of minutes.  The point is to get 1 full bathtub  =  1.

Filling + Emptying  =  1 Bathtub

(1/16)n  -  (1/20)n  =  1

Multiply each term by 320:

320(1/16)n - 320(1/20)n  =  320(1)

20n - 16n  =  320

4n  =  320

--->   n  =  80 minutes

geno3141  Apr 27, 2015
#1
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Are these questions serious......

zegroes  Apr 27, 2015
#2
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People are turning math into a joke its not my fault :(

Guest Apr 27, 2015
#3
+17745
+10

Since the bathtub can be filled in 16 minutes, the rate is 1 bathtub / 16 minutes  or  1/16.

Since the bathtub can be emptied in 20 minutes, the rate is -1 bathtub / 20 minutes  or  -1/20.

Let  n  be the number of minutes.  The point is to get 1 full bathtub  =  1.

Filling + Emptying  =  1 Bathtub

(1/16)n  -  (1/20)n  =  1

Multiply each term by 320:

320(1/16)n - 320(1/20)n  =  320(1)

20n - 16n  =  320

4n  =  320

--->   n  =  80 minutes

geno3141  Apr 27, 2015
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good job geno! :)

BrittanyJ  Apr 27, 2015
#5
+93656
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Thanks Geno,

I always like these questions.   I have to think EVERY time.

Melody  Apr 27, 2015
#6
+89953
+5

Here's another way to do this:

Each minute, the fractional amount that the tub is being filled = [1/16 - 1/20] = [20 - 16 / 320]  = 4/320

Now.....invert the fraction  =  320 / 4   = 80 minutes .....and that's how long it takes to fill the tub....

CPhill  Apr 27, 2015