Question

I'll really appreciate the help! A city plans to build a freeway to connect two major interstate highways. There are two construction companies (company A and company B) are available to do the project. If company A works alone for 40 days, it takes company B 28 days to finish the remaining by itself. If company A and company B work together, it takes 35 days to finish the project. If company A works alone for 30 days, how many days does it take company B to finish the job by itself?

Answer 1

To find how many days it takes company B to finish the job by itself, we can use the concept of work rate. By solving two equations representing different scenarios, we can find the individual work rates of Company A and Company B and calculate the desired result.

Step-by-step explanation:

To solve this problem, we can use the concept of work rate. Let's assume that company A's work rate is represented by 'a' and company B's work rate is represented by 'b'.

We know that if company A works alone for 40 days, it takes company B 28 days to finish the remaining work by itself. Using the equation 1/a + 1/b = 1/40 + 1/28, we can find the combined work rate.

We also know that if company A and company B work together, it takes 35 days to finish the project. Using the equation 1/a + 1/b = 1/35, we can find the combined work rate.

By solving these two equations, we can find the individual work rates of company A and company B. Company A's work rate is 1/70 and company B's work rate is 1/140. Therefore, if company A works alone for 30 days, it will take company B 42 days to finish the job by itself.