Rate problem

bharathh wrote:Working together at their respective constant rates, A and B can fill an empty tank in 1/2 hr. What is the constant rate of B?

1) Constant rate of A = 25 liters/min
2) Tank capacity = 1200 liters

I do not have an OA for this question. I'd like to see how you guys approach it.

r * t = w
Ra +Rb * 1/2 hr = work .. lets assume it's 1L

Ra +Rb = 2L/hr

Statement 2.. the tank capacity does not matter
Statement 1.. Since Ra is given .. we can find Rb using this eq Ra +Rb = 2L/hr..

sufficient..

IMO A

Ok.. I think the answer is C

Here's why

A is not sufficient on its own

So we are told that A and B work together to get something done in 1/2 hrs

1/A + 1/B = 1/30

ok great let's take a look at the statements

Statement 1

A's constant rate is 25 L/min.

Now although I was tempted to plug in A=25 L/min, I realized I could not do that.

Why? Because of the units. It says liters per min. We assume that A is time or min. Not L/min.

So our new equation should be

Rate of A + Rate B = Capacity of the tank/time to fill it up.

Let the tank at full capacity have C liters

25 L/min + Rate B (L/min) = C/30

This is obviously not sufficient to solve for B

Statement 2 is not sufficient as well because we don't know either rate.

However combining statements 1 and 2 we can plug in a value for capacity in the equation and solve.

Thus C

Solving just for giggles

30*rate of B = 1200 - 30*25

B = 15 L/min

I came up with C too.

I came up with C too.

Working together at their respective constant rates, A and B can fill an empty tank in 1/2 hr. What is the constant rate of B?

1) Constant rate of A = 25 liters/min
2) Tank capacity = 1200 liters

Yes, (C) is correct. Here is the most efficient way to think about this question.

Step 1) Recognize this is a typical distance = rate * time question. Technically they use the term "capacity"--but really the concept is the same.

Step 2) Recognize there are two components that combine into a total so it's a little bit trickier. This means we need to use one of our "special" formulas:

a) rate (A) + rate (B) = rate (total)
The rates must add up!

or b) 1/time(A) + 1/time(B) = 1/time(total)

Pick whichever one works best for you. Let's say we choose (a)

Step 3) rate (A) + rate (B) = rate (total)
We know [rate (A)].
We're supposed to find [rate (B)].
Do we know the last one: [rate (total)]?? If we do, then we have enough information.

No we don't know the combined rate. But do we know anything else about the total that might help us find the combined rate?
We know the combined total time was 1/2 hr.

And we know [rate = distance / time]. We know time, so all we need is the distance--then we'll find the total rate that we need. But as it stands now, there's not enough info in only statement 1 so the answer is not (A)

Step 4) Now what about if we knew statement 2 but did not know statement 1? Same thing. That means the answer is not (B)
In this equation: rate (A) + rate (B) = rate (total)
We need 2 terms in order to find the 3rd missing term.

Step 5) We need both rate (A) AND rate(total). In order to find rate(total) we'll need the distance ("capacity")--which is statement 2.

Therefore, we need both statements (1) and (2)--so the answer is (C).

Notice we did not have to do any calculations. In fact, calculations slow you down. You should be able to answer this question in less than 2 minutes.