Find an equation for the situation

Question

The time needed to paint a fence varies directly with the length of the fence and indirectly with the number of painters. If it takes five hours to paint 200 feet of fence with three painters, how long will it take five painters to paint 500 feet of fence 

Answer 1

Direct variation between two variables means they are equal, with a constant factor.

Inverse variation means one equals the other's reciprocal, again with a constant factor.

You can combine these to form a single equation. Here you have

T ∝ L

T ∝ 1/N

T = k L/N

 

(∝ is the symbol that represents variation)where T is the time, L is the length, N is the number of painters, and k is the constant factor.

 

You have two sets of information. If L = 200 ft and N = 3 painters then T = 5 hrs. You can plug these in to find the constant k.

 

Now that you know k, you can plug in your second situation with N = 5 painters and L = 500 ft to solve.