Abathtub can hold a maximum of 50 gallons of water. water can be drained out of the tub at a rate of 2 gallons per minute. if the tub is initially completely filled by a faucet at a rate of 1 gallon per minute, how long will it take to drain the full tub if the drain is opened but the faucet is kept on?

50 minutes

Step-by-step explanation:

Given,

Water can be drained out of the tub at a rate of 2 gallons per minute,

So, the drained water in 1 minute = 2 gallon,

That is, change in 1 minute = -2 gallon

( negative sign shows losing water)

Also, it is filled by a faucet at a rate of 1 gallon per minute,

So, the filled water in 1 minute = 1 gallon,

That is, change in 1 minute = + 1 gallon

( Positive sign shows additional water ),

Thus, total change in 1 minute = -2 + 1 = -1 gallon,

Let x be the time after which the bathtub will be emptied completely,

Total change in x minutes = -x gallon,

Bathtub will be emptied, if,

Initial volume of water + total change in water = 0

50 - x = 0  ( given volume of tub is 50 gallon )

Hence, it will take 50 minutes to drain the full tub.

fd

step-by-step explanation:

faster, im not sure why but i know it is faster