Suppose that the number of cars manufactured at an automobile plant varies jointly as the number of workers and the time they work. If 340 workers can produce 204 cars in 4 hours, find the number of cars that 400 workers can produce in 3 hours.

Question

Suppose that the number of cars manufactured at an automobile plant varies jointly as the number of workers and the time they work. If 340 workers can produce 204 cars in 4 hours, find the number of cars that 400 workers can produce in 3 hours.

Answer 1

Let's set up the equation first:

Number of cars = k * number of workers * time

where k is a constant of proportionality.

Using the information given:

204 = k * 340 * 4

Solving for k:

k = 204 / (340 * 4)
k = 0.015

Now we can use this constant to find the number of cars that 400 workers can produce in 3 hours:

Number of cars = 0.015 * 400 * 3
Number of cars = 180

Therefore, 400 workers can produce 180 cars in 3 hours.