Question

Four pipes can fill a tank in 70 minutes. How long will it take to fill the tank if 7 pipes are used?

Answer 1

Hint: We must first assume a variable (say $x$) that depicts the rate at which fluid flows from one pipe. We can then use the information that 4 pipes take 70 minutes to fill the tank, to find the volume of the tank. We will again have to assume a variable (say $t$) that is the time taken to fill the tank by 7 pipes. Hence, by equating the volume in two cases, we can find the value of variable $t$.

Complete step-by-step solution:
Let us assume that a pipe can fill $x$ litres in 1 minute, that is, $x$ litres per minute.
So, we can say that 4 pipes can fill $4x$ litres in 1 minute, that is, $4x$ litres per minute.
We are given that 4 pipes take 70 minutes to fill the tank.
So, we can easily write that in 70 minutes, 4 pipes will fill = $70\times 4x$ litres.
Thus, we can say that the total volume of the tank = $280x$ litres.
Now, since we know that 1 pipe fills $x$ litres per minute, so we can very well say that 7 pipes will fill the tank at the rate of $7x$ litres per minute.
Again, let us assume that the time taken to fill the tank by 7 pipes is $t$ minutes.
So, we can say that in $t$ minutes, 7 pipes will fill = $7xt$ litres.
But we had assumed that in $t$ minutes, the tank is completely filled. So, $7xt$ litres must be equal to the volume of the tank, which is $280x$ litres.
Thus, we can write
$7xt=280x$
Cancelling the terms from both sides, we get
$t=40$ minutes.
Hence, we can say that 7 pipes can fill the tank in 40 minutes.

Note: We can also solve this problem without having to assume any extra variable, using the following approach. We know that 4 pipes can fill the tank in 70 minutes. So, we can say that 1 pipe will tank in $70\times 4=280$ minutes. And thus, 7 pipes can fill the tank in $\dfrac{280}{7}=40$ minutes.