It takes 4 workers five days to clean 180 miles of highway. How many workers are needed to clean 250 miles of highway in just 6 days?
To determine the number of workers needed to clean 250 miles of highway in 6 days, we can set up a proportion based on the given information.
First, let's calculate the work rate of the 4 workers who can clean 180 miles of highway in 5 days.
Work rate = (Miles cleaned) / (Number of workers * Number of days)
Work rate = 180 miles / (4 workers * 5 days)
Work rate = 9 miles per worker per day
Next, we can set up a proportion to find the number of workers needed to clean 250 miles in 6 days.
(Work rate for the given situation) = (Miles to be cleaned) / (Number of workers * Number of days)
9 miles per worker per day = 250 miles / (Number of workers * 6 days)
Now, we can solve for the number of workers.
9 * Number of workers * 6 = 250
54 * Number of workers = 250
Number of workers = 250 / 54
Number of workers ≈ 4.63
Since we cannot have a fraction of a worker, we need to round up to the nearest whole number.
Therefore, at least 5 workers are needed to clean 250 miles of highway in 6 days.
To find the number of workers needed to clean 250 miles of highway in 6 days, we can use the concept of man-hours. Man-hours refer to the number of hours worked collectively by all workers.
First, let's determine how many man-hours it takes to clean 180 miles of highway in 1 day. Since it takes 4 workers 5 days to clean 180 miles, the total man-hours for this task is 4 workers × 5 days = 20 worker-days.
Next, we can calculate the number of man-hours required to clean 250 miles in 6 days. Let's denote the number of workers needed by x. Using the information we have, we can set up a proportion:
180 miles / (4 workers × 5 days) = 250 miles / (x workers × 6 days)
Simplifying the proportion, we get:
180 / 20 = 250 / (6x)
Cross-multiplying, we have:
180 × 6x = 20 × 250
1080x = 5000
Dividing both sides of the equation by 1080, we find:
x = 5000 / 1080
x ≈ 4.63
Therefore, approximately 4.63 workers are needed to clean 250 miles of highway in 6 days. Since we can't have a fraction of a worker, we need to round up to the nearest whole number. Thus, you would need 5 workers.