suppose that it takes 100 workers 6 weeks to build 4 miles of highway. how many miles of highway could 160 workers build in 15 weeks

Question

suppose that it takes 100 workers 6 weeks to build 4 miles of highway. how many miles of highway could 160 workers build in 15 weeks

Answer 1

it takes 600 worker-weeks (like man-hours) to build 4 mi of highway

150 worker-weeks per mile

so 2400 worker-weeks can build
... 2400 / 150

Answer 2

To solve this problem, we can use the equation:

Workers × Time = Miles

For the first scenario, with 100 workers building 4 miles in 6 weeks, we have:

100 × 6 = 4

Now we can calculate the number of miles that can be built by 160 workers in 15 weeks:

160 × 15 = X (unknown value)

To find X, we need to set up a proportion using the previous equation:

100 × 6 = 160 × 15

Now we can solve for X:

600 = 2400

X = (2400 × 4) ÷ 600

X = 16 miles

Therefore, 160 workers could build 16 miles of highway in 15 weeks.

Answer 3

To calculate the number of miles of highway that 160 workers could build in 15 weeks, we can use the concept of "worker-weeks." A worker-week represents the amount of work one worker can complete in one week.

First, we need to find the worker-weeks required to build 4 miles of highway with 100 workers in 6 weeks. This can be calculated as follows:

Worker-weeks = Number of workers * Number of weeks
Worker-weeks = 100 workers * 6 weeks
Worker-weeks = 600

So, it took 600 worker-weeks to build 4 miles of highway.

Next, we need to calculate the number of worker-weeks required to build the desired number of miles with 160 workers in 15 weeks:

Number of worker-weeks = Number of workers * Number of weeks
Number of worker-weeks = 160 workers * 15 weeks
Number of worker-weeks = 2400

Now, we have the worker-weeks required to build the desired number of miles. To find the number of miles, we need to divide the worker-weeks by the worker-weeks per mile ratio:

Number of miles = Number of worker-weeks / Worker-weeks per mile

Worker-weeks per mile = Worker-weeks / Number of miles
Worker-weeks per mile = 600 worker-weeks / 4 miles
Worker-weeks per mile = 150 worker-weeks per mile

Finally, we can calculate the number of miles of highway that 160 workers could build in 15 weeks:

Number of miles = Number of worker-weeks / Worker-weeks per mile
Number of miles = 2400 worker-weeks / 150 worker-weeks per mile
Number of miles = 16 miles

Therefore, 160 workers could build 16 miles of highway in 15 weeks.