Question

If a pipe can fill a tank in 2 hours and another pipe can fill the same tank in 40 minutes.how much time in minutes is needed to fill the tank if both the pipe are working together?

Answer 1

Both pipes will fill the tank in 30 minutes.

Explanation:

Let's do the setup first:
1) The tank has a capacity of X (The unit doesn't matter here)
2) The rate that each pipe fills the tank is `R_1` for the first pipe and `R_2` for the second pipe.

Now, we know that the first pipe fills the tank in 2 hours. That means that the tank's capacity divided by the fill rate of the first pipe is equal to 2 hours (since we need the answer in minutes I'll use minutes here, so 120 minutes):

`X/R_1=120`

The rate of the second pipe gives us:

`X/R_2=40`

Solving both for X:

`X=120R_1` and `X=40R_2`

If we set the Xs equal to each other we get:

`120R_1=40R_2`

`120/40R_1=R_2`

`3R_1=R_2`

Now for the equation we have to solve. We need to know how much time (T) `R_1 + R_2` are going to take to fill the tank. That looks like this:

`T=X/(R_1+R_2)`

So we know that `X=120R_1` and that `R_2=3R_1` so substituting those values we get:

`T=(120R_1)/(R_1+3R_1)`

`T=(120R_1)/(4R_1)`

Both `R_1` cancel out, so:

`T=120/4=30`