Question

If $7$ pipes can fill a take in $1$ hour $24$ minutes, how long will it take to fill the tank if $6$ pipes of the same type are used?

Answer 1

It is given that $7$ pipes can fill a tank in $84$ minutes. Let $6$ pipes fill the tank in $x$ minutes. Clearly more pipes will fill the tank in less time. So it is a case of inverse proportion. If $7$ pipes can fill the tank in $84$ minutes, it takes $7\times 84$ minutes for one pipe to fill the tank. Now $7$ is inversely proportional to $84$ and the constant of proportionality is $k=7\times 84$. Since $6$ pipes can fill the tank in $x$ minutes, we must have $6\times x=k$. Thus we obtain
$x=\frac{7\times 84}{6}=98$.
Hence it takes $98$ minutes for $6$ pipes to fill the tank; i.e., $1$ hour $38$ minutes.