Question

A construction team gives an estimate of three months to repave a large stretch of a very busy road. The government responds that it's too much inconvenience to have this busy road obstructed for three months, so the job must be completed in one month. How does this deadline change the number of workers needed?

A) One-ninth as many workers are needed.B) One-third as many workers are needed.C) The same number of workers are needed.D) Three times as many workers are needed.E) Nine times as many workers are needed.

Answer 1

Answer: D) Three times as many workers are needed

Step-by-step explanation:

The number of worker that can complete the task in 3 months needs to be trippled if they want to complete the task in one month.

For example, let x represent the rate at which a number of workers needed to complete the task a in 3months works.( In per month)

The rate at which x works is;

x = a/3

That is in one month they complete one-third of the task.

But when we triple the number of workers, their rate also triples.

3×x = 3 × a/3

3x = a

Meaning three times the worker will complete task a in one month.

Therefore, three times the number of the workers will finish the task in one month.

Answer 2

D) Three times as many workers are needed

Step-by-step explanation:

Let the number of workers needed for this project be x. Then the total number of man-month needed for this project originally (3 months) is x * 3 = 3x man month. Now since the government wants to reduce the time length from 3 months to 1 month then the new number of workers needed is

3x / 1 = 3x

So 3 times the original amount. D) is the correct answer