Tap 1 takes 1.5 hours to fill a certain tank with water. Tap 2 fills

Question

Tap 1 takes 1.5 hours to fill a certain tank with water. Tap 2 fills the same tank with water at a rate X times as fast as Tap 1. Tap 1 and Tap 2 together take 15 minutes to fill the same tank with water. Find the value of X.

A. 1/9
B. 1/5
C. 5
D. 9
E. 45

Show Answer

Official Answer

C

A. 1/9
B. 1/5
C. 5
D. 9
E. 45

imeanup · Answer

Method 1: Efficiency

Tap A takes  1.5  hrs i.e.  1.5 	imes 60 = 90   min to fill the tank when working individually and Tap (A+B) takes  15  min to fill the tank when working together.

The problem statement ask for the efficiency of Tap B i.e. X.

To find the efficiency, we need to find the  LCM(A, A+B) = lcm(90, 15) = 90 . (Also, called total work. Review my pervious post on "Time and work" to understand better.)
The efficiency of  A = \dfrac{90}{90} = 1  and (A+B)'s  = \dfrac{90}{15} = 6 .

Therefore,  A = 1  and  A+ B = 6 , solving  B = 6 - 1 = 5 .

C

If you don't understand, then REPEAT Please!

btsaami · Answer

1/1.5 + X/1.5= 60/15 (Taking time in hours)

(1+X)/1.5= 60/15

Therefore 1+X= 60/10 , X= 5

Addu.23 · Answer

I'm confused with this line "Tap 2 fills the same tank with water at a rate X times as fast as Tap 1". Doesn't this mean Tap 2 = xT1 + T1?

Such lines are a weak point for me. Can someone share a list of such lines and it's equation or provide a link to such a list? In my notes I have these 2 lines:
'A's speed is 1.5 times B's speed' -> a=1.5b
'A's speed is 1.5 times faster than B's speed' -> a= 1.5b + b

Bunuel  would appreciate if you can help here

Bunuel · Answer

Both of these mean the same thing:

(Speed of A) = 1.5(Speed of B)

Here is my post from another topic addressing this issue:

Agree that it's confusing but check below:

Merriam Webster's  Dictionary of English Usage :

The argument in this case is that  times more  (or  times larger ,  times stronger ,  times brighter , etc.) is ambiguous, so that "He has five times more money than you" can be misunderstood as meaning "He has six times as much money as you." It is, in fact, possible to misunderstand  times more  in this way, but it takes a good deal of effort. If you have $100, five times that is $500, which means that "five times more than $100" can mean (the commentators claim) "$500 more than $100," which equals "$600," which equals "six times as much as $100." The commentators regard this as a serious ambiguity, and they advise you to avoid it by always saying "times as much" instead of "times more." Here again, it seems that they are paying homage to mathematics at the expense of language. The fact is that  "five times more" and "five times as much" are idiomatic phrases which have - and are understood to have - exactly the same meaning .

The "ambiguity" of  times more  is imaginary : in the world of actual speech and writing, the meaning of  times more  is clear and unequivocal. It is an idiom that has existed in our language for more than four centuries, and there is no real reason to avoid its use.

More on this  here .

Also, check the following posts by Ianstewart:

To summarize, I think the actual wording on the GMAT will always use " times as many " (at least in quant section), so you should not worry about it.

unraveled · Answer

Here's a few cents from my side to brainstorm a little bit.
Assuming you understood the grammatical aspects that troubled you. So, my inputs is only for conceptual aspect. Hope you don't mind.

Quesiton is:
Tap 1 takes 1.5 hours to fill a certain tank with water. Tap 2 fills the same tank with water at a rate X times as fast as Tap 1. Tap 1 and Tap 2 together take 15 minutes to fill the same tank with water. Find the value of X.

A. 1/9
B. 1/5
C. 5
D. 9
E. 45

Conceptually, you see that 2 fills the tank X times that of 1 i.e. X >=1 (X = 2 or 3 or 4 or 5.... so on if we consider integer only to avoid the complexity of fractions). And we don't need to calculate.

Now, if 1 takes 6 times(90/15) the time that 1 and 2 together take to fill the tank then that means that speed of filling the tank by the two taps too would make a sum of 6. And in this sum of 6, 1 part belongs to Tap 1 and rest 5 parts belong to Tap 2. Just that you have to know that here speed and time are inverse to each other so X has to be chosen.

Hence X = 5. Here we have our answer.

Solution by equation : Let 100 is work i.e. total tank water that fill it.
So, Speed of Tap 1 =  \frac{100}{90} 
Speed of Tap 2 =  \frac{100X}{90}

Solving for equation
 \frac{Total Water }{ Speed of Tap 1 + Speed of Tap 2} = 15 
 100/(\frac{100}{90} +\frac{100X}{90}) = 15 
X = 5
So, Tap 2 was 5 times faster than Tap 1.
OR
Tap 2 filled  \frac{5}{6}^{th}  part of the tank and Tap 1  \frac{1}{6}^{th} .

Similarly, If you just replace 15 by any number ( if a factor of 90 it is better) you would get X's value accordingly.
Like if we replace 15 by 30 then X = 2, meaning 2's speed was twice that of 1's. Here Tap 1 would have taken 3 times the time the two together would have taken.

Point is the slower tap makes only 1 part of the total parts that we may get. Will leave upto you to do calculations for the non factor of 90.

Note: Among the choices we have A and B are not possible since it would have made Tap 2 slower than Tap 1 because Tap 2's speed cannot be less than 1 already. And you can put C,D or E values to solve for 15 minutes.

Hope this helps.

Tap 1 takes 1.5 hours to fill a certain tank with water. Tap 2 fills

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Tap 1 takes 1.5 hours to fill a certain tank with water. Tap 2 fills

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards