A Small Water Pump Would Take 2 Hours To Fill An Empty Tank GMAT Problem Solving

​Question - A small water pump would take 2 hours to fill an empty tank. A larger pump would take 1/2 hour to fill the same tank. How many hours would it take both pumps, working at their respective constant rates, to fill the empty tank if they began pumping at the same time?

1. 1/4
2. 1/3
3.  2/5
4. 5/4
5. 3/2

“A small water pump would take 2 hours to fill an empty tank” - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMATOfficial Guide”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

Solution and Explanation

Approach Solution 1

These major ideas are necessary to tackle rate problems consistently:
- Each circumstance has a unique rate calculation;
-If you collaborate, sum the rates.
- Instead of using 1 and utilising fractions where it states "a—-" (a pool, a job, a tank, a wall, etc.), choose a number to represent the units:
therefore, it takes a small pump two hours to fill an empty tank.
Decide on 6 as the number of gallons in the tank, then set up (Rs)(2) = 6 so that Rs = 3.
The same tank may be filled by a huge tank in half an hour, hence Rl(.5) = 6 and Rl= 12.
Then
How long should they fill the tank if they cooperate:
(12 + 3)(T)= 6
t = 6/15
= 2/5
The answer is C which is 2/5

Correct Answer: C

Approach Solution 2

There is another approach to solve the question
It is Implied:

1. It would take a tiny water pump two hours to fill an empty tank.
2. It would take a larger pump half an hour to fill the same tank.

It is asked
If both pumps started pumping at the same moment and continued to operate at their respective constant rates, how long would it take to fill the empty tank?

1. It would take a tiny water pump two hours to fill an empty tank.

A simple water pump will fill half of the tank in an hour.

2. It would take a larger pump half an hour to fill the same tank.

A small water pump will fill two tanks in one hour.
Together, the tiny and huge pumps will fill 2.5 of the tanks in an hour.
Total time needed to fill the empty tank is 1/2,5 = 2/5 hours.
The answer is C which is 2/5

Correct Answer: C

Approach Solution 3

This problem required a consistent way to approach rate problems:

1.  each situation gets it's own rate formula
2.  if work together, add the rates
3. If it says "a---" (a pool, a job, a tank, a wall etc.) then pick a number to represent the units

Here the problem can be solved:
a small pump takes 2 hours to fill an empty tank
so, picking 6 as the number of gallons in the tank becomes (Rs)(2) = 6 so Rs = 3
a large tank can fill the same tank in 1/2 hour - Rl(.5) = 6 so Rl= 12
if they work together how long to fill the tank it becomes (12 + 3)(T)= 6 or t = 6/15 = 2/5

Correct Answer: C

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