Question

One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill the tank in \[36\] minutes, then the slower pipe alone will be able to fill the tank in how many minutes?

Answer 1

Hint: Here, we are asked to find the time taken by the slower pipe to fill the tank. So, we will consider it as \[x\] minutes. Then from the given data we will calculate the time required by the other pipe. After that we will find part of the tank filled by the slower pipe in one minute and similarly the part of the tank filled by the other pipe in one minute. Then we will add them and equate with the actual part of the tank filled in one minute.

Complete step by step solution:
Let, the time taken by the slower pipe to fill the tank \[ = x\] minutes
Since the other pipe is three times faster, the time required will be less by three times.
\[\therefore \] the time required by the faster pipe to fill the tank \[ = \dfrac{x}{3}\] minutes
Now, since the slower pipe fill the whole tank in \[x\] minutes,
\[\therefore \] the part of tank filled by slower pipe in \[1\] minute \[ = \dfrac{1}{x}\]
Similarly,
The part of tank filled by the faster pipe in \[1\] minute \[ = \dfrac{3}{x}\]
Now since they are filling the tank together,
\[\therefore \] the part of the tank filled by both the pipes working together in one minute \[ = \dfrac{1}{x} + \dfrac{3}{x}\]
Now in the question it is given that both the pipes working together fills the tank in \[36\] minutes.
\[\therefore \] the part of the tank filled by both the pipes working together in one minute \[ = \dfrac{1}{{36}}\]
But above we derived that,
the part of the tank filled by both the pipes working together in one minute \[ = \dfrac{1}{x} + \dfrac{3}{x}\]
so, these must be equal and hence we can equate them. So, we get;
\[ \Rightarrow \dfrac{1}{x} + \dfrac{3}{x} = \dfrac{1}{{36}}\]
Now we will take \[x\] as the LCM and solve it further. We get;
\[ \Rightarrow \dfrac{4}{x} = \dfrac{1}{{36}}\]
Now we will shift \[x\] to the RHS.
\[ \Rightarrow 4 = \dfrac{x}{{36}}\]
On simplification we get;
\[ \Rightarrow x = 36 \times 4\]
\[ \Rightarrow x = 144\]
Hence the time required by the slower pipe to fill the tank alone is \[144\] minutes.
So, the correct answer is “ \[144\] minutes”.

Note: Here, one thing to note is that, less efficiency means more time and more efficiency means less time. As we can see in the given question, the slower pipe that is the less efficient pipe takes three times more time than the time taken by the faster pipe which is also the more efficient pipe.
If two persons A and B do the same work separately and if efficiency of A is two times that of B, then, if A completes that work in \[n\] days, then B will complete the same work in \[2n\] days.