4. Jean and Mark are going to fill a pool with 2 different sized hoses. Jean can fill the pool in 4 hours, while Mark can complete it in 6 hours. Their supervisor thinks that the job will take 5 hours to complete if they work together. Explain each step in solving this equation, and determine if the supervisor is correct or not.

2.4 hours.

Step-by-step explanation:

Remark

The supervisor is not quite correct. The correct answer must be lower than the lowest number, otherwise you are taking out what the person with the narrower hose must be taking out what the other person is putting in.

Equation

Let x = the amount of time needed for him to fill the pool

Let y = the amount of time needed for the second person to fill the pool

Let z = the amount of time needed for both to fill the pool.

1/x + 1/ y = 1/z

1/4 + 1/6 = 1/z         The common denominator is 12

3/12 + 2/12 = 1/z

5/12 = 1/z                Cross multiply

5z = 12 * 1               Divide by 5

z = 12/5

z = 2 2/5

z = 2.4 hours