Question

A full 200-gallon tank of water is leaking 0.5 gallons of water an hour, and an empty tank is being filled at a rate of 4 gallons an hour. How many hours, h, will it take for the two tanks to hold the same amount of water?

a) 40 hours
b) 50 hours
c) 60 hours
d) 70 hours

Answer 1

It will take approximately 44.4 hours for the two tanks to hold the same amount of water.

Step-by-step explanation:

To find the number of hours it will take for the two tanks to hold the same amount of water, we need to set up an equation.

Let x be the number of hours it takes for the tanks to hold the same amount of water.

The amount of water leaked from the full tank can be represented as 0.5x gallons.

The amount of water filled into the empty tank can be represented as 4x gallons.

Since the two tanks will hold the same amount of water when they contain the same amount of water, we can set up the equation 200 - 0.5x = 4x.

Solving this equation will give us the value of x, which represents the number of hours it will take for the two tanks to hold the same amount of water.

Let's solve the equation:

• 200 - 0.5x = 4x
• 200 = 4.5x
• x = 200/4.5
• x ≈ 44.4

Therefore, it will take approximately 44.4 hours for the two tanks to hold the same amount of water.