The time it takes to clean the house varies inversely with the number of people cleaning. If it takes 1 person 4 hours to clean the house, how long will it take 3 people?
12 hours
Your answer doesn't make sense.
I somehow typed 12 because I saw a 4 and 3
So how would you set up the equation
Don't worry about an equation. Use your head and figure it out. I'm sure you can come close by estimating.
To solve this problem, we need to use the concept of inverse variation.
Inverse variation means that as one quantity increases, the other quantity decreases, and vice versa. Mathematically, this can be represented by the equation y = k/x, where y is one quantity, x is the other quantity, and k is the constant of variation.
In this case, the time it takes to clean the house (y) varies inversely with the number of people cleaning (x). We are given that it takes 1 person 4 hours to clean the house.
Let's set up the equation using the given information:
4 = k/1
To solve for k, we can multiply both sides of the equation by 1:
4 * 1 = k * 1
4 = k
Now we have the value of k.
To find out how long it will take 3 people to clean the house, we can substitute the values into the equation:
y = k/x
y = 4/3
So, it will take 3 people 4/3 (or 1 and 1/3) hours to clean the house.
Alternatively, if you prefer to directly calculate the answer, you can simply multiply the initial time (4 hours) by the initial number of people (1) and divide by the desired number of people (3):
(4 hours * 1 person) / 3 people = 12 hours
Therefore, it will take 3 people 12 hours to clean the house.