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

fabric (square meters)                   cloaks

7                                                           21

4/3                                                         4

step-by-step explanation:

we are told that harry needs 2 square meters of fabric for every 6 wizard cloaks he makes.

1. first of all we will find how many cloaks can be made from 1 square meter of fabric by dividing 6 by 2.

we can see that 3 cloaks can be made from 1 square meter of fabric. now we will multiply 3 by 7 to find number of cloaks made from 7 square meters of fabric.

therefore, harry will make 21 cloaks from 7 square meters of fabric.

2. let us find how many square meters of fabric will be needed to make 4 cloaks.

first of all we will find fabric needed for 1 cloak by dividing 2 by 6.

we can see that fabric needed for 1 cloak is   square meter. now we will multiply   by 4 to find fabric needed for 4 cloaks.