Pipe A fills a swimming pool in 4 hours. Pipe B empties the pool in 6 hours. If pipe A was opened at 8:00 am and Pipe B at 9:00 am, at what time will the pool be full?

A. 15:00
B. 17:00
C. 18:00
D. 19:00
E. 20:00
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

IMO C

Time to fill = Total Job/Combined Rate

Combined Rate = 1/4 - 1/6

Total Job = 3/4 ( As 1/4 is already filled in 1 hour gap)

Thus Time = 9 hours, and ans C.

Please correct if the method is wrong.

Pipe A fills the pool in 4 hrs.
1 hour's work : 1/4

Pipe B empties the pool in 6 hrs.
1 hour's work : 1/6

Together if they work, 1 hour's work = 1/4 -1/6 = 1/12

Given : Pipe A started at 8:00 a.m and Pipe B at 9:00 a.m
Pool filled after 1 hour by Pipe A : 1/4 or 3/12

After 9:00 a.m
Pool filled after 1 hour with both the pipes on : 1/12
Pool filled after 9 hours with both pipes on : 9/12

Pool filled in 1 hour + Pool filled in 9 hours = 3/12 +9/12 =1

Therefore, it takes 10 hrs to fill the pool

As Pipe A started at 8:00 a.m, pool is full at 18:00 hrs

Answer is C.
_________________

"I would risk the fall, just to know how it feels to FLY"

This is an easy question if done carefully.

so in the first hour, 1/4 of pool is full.
from the next hour (9 am onwards), let it take x hours to fill the pool.

So,

1/4 + (1/4 - 1/6)*x = 1
solving x we get x = 9.

Hence after 9 am it takes 9 hours ie 6 pm or 1800 hours.

We are given that pipe A fills a swimming pool in 4 hours and pipe B empties the pool in 6 hours. Thus, the fill rate of pipe A is 1/4 and the empty rate of pipe B is 1/6.

Since pipe A was opened at 8 a.m. and pipe B was at 9 a.m., we can let the time of pipe A = t + 1 and the time of pipe B = t. Also, we will subtract the work of pipe B (emptying) from the work done by pipe A (filling) to get the net amount of filling:

(1/4)(t + 1) - (1/6)(t) = 1

t/4 + 1/4 - t/6 = 1

Multiplying by 12, we have:

3t + 3 - 2t = 12

t = 9

So, the pool will be filled at 9 a.m. + 9 hours = 18:00.

Answer: C
_________________

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources