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 hours required for 400 workers to produce 180 cars.
If the number of cars varies jointly as the number of workers and time worked, we can write:
C = k * W * T
where C is the number of cars, W is the number of workers, T is the time worked, and k is the constant of proportionality.
To find k, we can use the information given in the problem:
204 = k * 340 * 4
Solving for k, we get k = 0.15.
Now we can use this value of k to answer the second part of the question. We want to find the number of hours required for 400 workers to produce 180 cars, so we can write:
180 = 0.15 * 400 * T
Solving for T, we get T = 3 hours.
Therefore, it would take 400 workers 3 hours to produce 180 cars.