A tank has both an inlet pipe and an outlet pipe. Working..

This topic has expert replies
Legendary Member
Posts: 641
Joined: Tue Feb 14, 2012 3:52 pm
Thanked: 11 times
Followed by:8 members
Hello,

Can you please help with the following:

A tank has both an inlet pipe and an outlet pipe. Working alone, the inlet pipe can fill up the tank in 5 hours. Working alone, the outlet pipe can empty out the tank in 15 hours. If it is desired that the tank should be filled, from empty, exactly 6 hours after the inlet pipe is turned on at 9:30am, then at what time should the outlet pipe be opened ?

A)10:00am
B)10:45am
C)12:00pm
D)12:30pm
E)1:30pm

OA: D


Rate x Time = Work

Input Pipe: 1/5 x 5 = 1
Output Pipe: 1/15 x 15 = 1

So, rate at which the tank is getting filled is 1/5 - 1/15 = 2/15

However, I am stuck at this point. Can you please assist?

Thanks a lot,
Sri


Update:

I just tried solving as follows now:

The tank should be filled 6 hours after the inlet pipe is opened at 9:30 a.m. In these 6 hours, 1/5 x 6 = 6/5 of the tank is filled by the inlet pipe.

So we need to take the extra quantity out of the tank.

i.e. 6/5 - x = 1 => x = 1/5.

Hence, this extra 1/5 of the water needs to be removed by the outlet pipe.

So, for the outlet pipe 1/15 x t = 1/5
=> t = 3 hours.

Hence, it has to be turned 3 hours before 3:30 p.m. Hence, 12:30 p.m.

Is this approach correct? Also, is there a better way to solve this problem?

Thanks a lot,
Sri
Last edited by gmattesttaker2 on Sun Jun 15, 2014 5:29 pm, edited 1 time in total.

User avatar
Legendary Member
Posts: 1893
Joined: Sun May 30, 2010 11:48 pm
Thanked: 215 times
Followed by:7 members

by kvcpk » Sun Jun 15, 2014 5:24 pm
gmattesttaker2 wrote:Hello,

Can you please help with the following:

A tank has both an inlet pipe and an outlet pipe. Working alone, the inlet pipe can fill up the tank in 5 hours. Working alone, the outlet pipe can empty out the tank in 15 hours. If it is desired that the tank should be filled, from empty, exactly 6 hours after the inlet pipe is turned on at 9:30am, then at what time should the outlet pipe be opened ?

A)10:00am
B)10:45am
C)12:00pm
D)12:30pm
E)1:30pm

OA: D


Rate x Time = Work

Input Pipe: 1/5 x 5 = 1
Output Pipe: 1/15 x 15 = 1

So, rate at which the tank is getting filled is 1/5 - 1/15 = 2/15

However, I am stuck at this point. Can you please assist?

Thanks a lot,
Sri
Following your approach,
Tank gets filled at 1/5 rate for t hours
and then it gets filled at 2/15 rate for 6-t hours.

1/5 * t + 2/15 * (6-t) = 1 (Since the tank should be full after 6 hours)
t/5 + 12/15 -2t/15 = 1
12/15 + t/15 = 1
t/15 = 3/15
t=3

Hence after 3 hours, outlet pipe should be opened.
Choose D

Hope this helps!!
"Once you start working on something,
don't be afraid of failure and don't abandon it.
People who work sincerely are the happiest."
Chanakya quotes (Indian politician, strategist and writer, 350 BC-275BC)

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Sun Jun 15, 2014 5:44 pm
gmattesttaker2 wrote:
A tank has both an inlet pipe and an outlet pipe. Working alone, the inlet pipe can fill up the tank in 5 hours. Working alone, the outlet pipe can empty out the tank in 15 hours. If it is desired that the tank should be filled, from empty, exactly 6 hours after the inlet pipe is turned on at 9:30am, then at what time should the outlet pipe be opened ?

A)10:00am
B)10:45am
C)12:00pm
D)12:30pm
E)1:30pm
Given: Inlet pipe FILLS the tank in 5 hours
Outlet pipe EMPTIES the tank in 15 hours

Let's choose a NICE NUMBER for the volume of the tank.
Let's say the tank has a total capacity of 15 gallons.

This means that inlet pipe FILLS the tank at a rate of 3 gallons/hour
And the outlet pipe EMPTIES the tank at a rate of 1 gallon/hour

So, in 6 hours, the inlet pipe (at 3 gallons/hour) will add 18 gallons to the tank. This is 3 gallons MORE than we need. So, we need the outlet pipe to remove those extra 3 gallons.
Since the outlet pipe EMPTIES the tank at a rate of 1 gallon/hour, we need to give the outlet pipe 3 hours to do its job.
So, we need to open the outlet pipe 3 hours BEFORE 3:30pm
In other words, we need to open the outlet pipe at [spoiler]12:30pm [/spoiler]

Answer: D

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image

User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Sun Jun 15, 2014 7:14 pm
A tank has both an inlet pipe and an outlet pipe. Working alone, the inlet pipe can fill up the tank in 5 hours. Working alone, the outlet pipe can empty out the tank in 15 hours. If it is desired that the tank should be filled, from empty, exactly 6 hours after the inlet pipe is turned on at 9:30am, then at what time should the outlet pipe be opened ?

A)10:00am

B)10:45am

C)12:00pm

D)12:30pm

E)1:30pm
Let the tank = 30 liters.

Rate for the inlet pipe = w/t = 30/5 = 6 liters per hour.
Rate for the outlet pipe = w/t = 30/15 = 2 liters per hour.
When the inlet pipe and the outlet pipe work together, the inlet pipe pumps IN 6 liters per hour, while the outlet pipe pumps OUT 2 liters per hour.
Thus, the NET rate for the 2 pipes working together = 6-2 = 4 liters per hour.

To fill the tank in 6 hours, the required average rate = w/t = 30/6 = 5 liters per hour.
The required average rate (5 liters per hour) is HALFWAY between the rate for the inlet pipe alone (6 liters per hour) and the rate for the 2 pipes working together (4 liters per hour).
Implication:
For 1/2 the time (3 hours) the inlet pipe must work alone.
For 1/2 of the time (the remaining 3 hours) the 2 pipes must work together.
Since the inlet pipe works alone for 3 hours, the outlet pipe is turned on 3 hours after the start time:
9:30am + 3 hours = 12:30pm.

The correct answer is D.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3