# Math Help - The bathtup-Problem

1. ## The bathtub-Problem

Hello!

I've encountered a difficult problem here and would like some help.
It would be great for my understanding If you could help me solve it with fractions.

A bathtub is filled in 5 minutes and emptied in 10 minutes when the plug is pulled out. How much time will it take to fill the bathtub if you forget to insert the plug?

2. ## Re: The bathtup-Problem

Originally Posted by Benjy
Hello!

I've encountered a difficult problem here and would like some help.
It would be great for my understanding If you could help me solve it with fractions.

A bathtub is filled in 5 minutes and emptied in 10 minutes when the plug is pulled out. How much time will it take to fill the bathtub if you forget to insert the plug?
rate tub is filled ... $\frac{1 \, tub}{5 \, min}$

rate tub is emptied ... $\frac{1 \, tub}{10 \, min}$

combined rate ... $\frac{1 \, tub}{5 \, min} - \frac{1 \, tub}{10 \, min} = ?$

3. ## Re: The bathtup-Problem

Originally Posted by Benjy
Hello!

I've encountered a difficult problem here and would like some help.
It would be great for my understanding If you could help me solve it with fractions.

A bathtub is filled in 5 minutes and emptied in 10 minutes when the plug is pulled out. How much time will it take to fill the bathtub if you forget to insert the plug?
I'm not sure whether there is a specific answer for this question, here is a try:

If x is defined as the volume of the bathtub, then x/5 is the speed of water inflow per minute and x/10 is the speed of water outflow per minute. Then you have a net inflow rate of y=(x/5-x/10).

Hope this helps

4. ## Re: The bathtup-Problem

Originally Posted by Vingar
I'm not sure whether there is a specific answer for this question ...
then you better have another look at post #2

5. ## Re: The bathtup-Problem

Originally Posted by Benjy
Hello!

I've encountered a difficult problem here and would like some help.
It would be great for my understanding If you could help me solve it with fractions.

A bathtub is filled in 5 minutes and emptied in 10 minutes when the plug is pulled out. How much time will it take to fill the bathtub if you forget to insert the plug?
This question is very simple. If the time it takes to empty is double the time it takes to fill, it should fill in 10 minutes, since its rate of fill was cut in half. Correct?

6. ## Re: The bathtup-Problem

Originally Posted by TheBoss
This question is very simple. If the time it takes to empty is double the time it takes to fill, it should fill in 10 minutes, since its rate of fill was cut in half. Correct?
yes It's correct

Thanks

7. ## Re: The bathtup-Problem

Originally Posted by skeeter
rate tub is filled ... $\frac{1 \, tub}{5 \, min}$

rate tub is emptied ... $\frac{1 \, tub}{10 \, min}$

combined rate ... $\frac{1 \, tub}{5 \, min} - \frac{1 \, tub}{10 \, min} = ?$
Thank you

I understand you

I first tried to fit it into the "distance=speed*time"-Formula but it didn't work for me

8. ## Re: The bathtup-Problem

Originally Posted by Vingar
I'm not sure whether there is a specific answer for this question, here is a try:

If x is defined as the volume of the bathtub, then x/5 is the speed of water inflow per minute and x/10 is the speed of water outflow per minute. Then you have a net inflow rate of y=(x/5-x/10).

Hope this helps

Thank you