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 220 workers can produce 198 cars in 5 hours, find the number of hours required for 175 workers to produce 189 cars.

Answer 1

First, we need to set up the relationship between the number of workers, the time they work, and the number of cars produced:

Number of cars = k * Number of workers * Time worked

Where k is a constant of proportionality.

Using the given information, we can set up the equation:

198 = k * 220 * 5

Solving for k:

k = 198 / (220 * 5) = 0.018

Now we can use this value of k to find the number of hours required for 175 workers to produce 189 cars:

189 = 0.018 * 175 * x

Solving for x:

x = 189 / (0.018 * 175) = 6

Therefore, it will take 175 workers 6 hours to produce 189 cars.