Tutors, sign in to answer this question.

rate *time=output

t=time

rate of fill *t=Volume of tank (filled)

rate of fill*9=V

rate of fill=V/9

rate of drain*t=Volume of tank(drained)

rate of drain*11=V

rate of drain=V/11

time needed to fill the tank with both drains open:

[(V/9)-(V/11)]*t=V

[(1/9)-(1/11)]*t=1

(2/99)*t=1

t=99/2 or 49.5 hrs

check: (99/2)*(1/9)=11/2=5 1/2 tanks filled

(99/2)*(1/11)=9/2=4 1/2 tanks drained

difference is 1 tank filled

Let's mark work, which must be done as

Productivity of the pipe-A is

Productivity of the pipe-B is

Tank fill rate is:

(1/9) - (1/11) = 2/99

Daric Matthew G. | Daric Matthew G.Daric Matthew G.

What we know:

It fills up faster than it drains

Variables:

X_{f} = amount of liquid in a full tank (units do not matter, pick one)

Equations:

x_{fill}(t)=(X_{f}/9)t

x_{fill}(0)=0

x_{fill}(9)=X_{f}

m=(X_{f}/9)

x_{empt}(t)=(-X_{f}/11)t_{
}

x_{empt}(0)=X_{f}

x_{empt}(11)=0

m=(-X_{f}/11)

Solve:

x_{total}(t)=x_{fill}(t) + x_{empt}(t)

= (X_{f}/9)t + (-X_{f}/11)t

= (11X_{f}/99)t - (9X_{f}/99)t_{
}

= (2X_{f}/99)t

set x_{total}(t)=X_{f}

X_{f} = (2X_{f}/99)t

Check:

Choose full tank = 1

xfill(t)=(1/9)t

xfill(0)=0

xfill(9)=1

m=(1/9)

xempt(t)=(-1/11)t

xempt(0)=1

xempt(11)=0

m=(-1/11)

xfill(0)=0

xfill(9)=1

m=(1/9)

xempt(t)=(-1/11)t

xempt(0)=1

xempt(11)=0

m=(-1/11)

xtotal(t)=xfill(t) + xempt(t)

= (1/9)t + (-1/11)t

= (11/99)t - (9/99)t

= (2/99)t

set xtotal(t)=1

1 = (2/99)t

**t=99/2**

= (1/9)t + (-1/11)t

= (11/99)t - (9/99)t

= (2/99)t

set xtotal(t)=1

1 = (2/99)t

*Edit

WHOOPS! I forgot to divide

Already have an account? Log in

By signing up, I agree to Wyzant’s terms of use and privacy policy.

Or

To present the tutors that are the best fit for you, we’ll need your ZIP code.

Your Facebook email address is associated with a Wyzant tutor account. Please use a different email address to create a new student account.

Good news! It looks like you already have an account registered with the email address **you provided**.

It looks like this is your first time here. Welcome!

To present the tutors that are the best fit for you, we’ll need your ZIP code.

Please try again, our system had a problem processing your request.

Kevin T.

A Laid Back Tutor who Specializes in Math, Science, and Test Prep

$11.25 per 15 min

View Profile >

Lisa T.

Experienced Tutor, Specializing in Math, Science and English

$11.25 per 15 min

View Profile >

Katherine N.

Experienced Tutor Specialized in English and Math

$10 per 15 min

View Profile >

## Comments