Alice can complete a certain job in 5 hours she had been working on the job for two hours when a friend came along. And helped her finish together they completed the job in 1 hr how long would it take alices friend to complete a job on her own. I have 1 fifth plus 1 over1 equals 1 over x for 1 and one fifth hours

2/5 + 1/5 + 1/x = 1

x = 5/2

To find out how long it would take Alice's friend to complete the job on her own, we can start by determining Alice's work rate, which is the proportion of the job she can complete in one hour. We can calculate this by dividing the amount of work Alice completes (1 job) by the time it takes her to complete it (5 hours):

Alice's work rate = 1 job / 5 hours = 1/5 job per hour

Next, we know that Alice worked on the job for 2 hours before her friend joined. Therefore, Alice completed:

Alice's work done = Alice's work rate * time worked
Alice's work done = (1/5 job per hour) * 2 hours
Alice's work done = 2/5 job

Since Alice and her friend together completed the job in 1 hour, Alice's friend must have completed the remaining work, which is:

Friend's work done = Total work - Alice's work done
Friend's work done = 1 job - 2/5 job
Friend's work done = 3/5 job

Now, we can find out how long it would take Alice's friend to complete the job on her own. We'll let x represent the time it takes for the friend to complete the job:

Friend's work rate = Friend's work done / time taken
Friend's work rate = (3/5 job) / x hours

We are given the equation 1 + 1/5 = 1/x, which represents the combined work rate of Alice and her friend working together.

1 + 1/5 = 1/x

To solve this equation for x, we can cross-multiply:

5(1) + (1) = 5(1/x)
5 + 1 = 5/x
6 = 5/x

Now, we can solve for x by cross-multiplying again:

6x = 5

Dividing both sides by 6:

x = 5/6

Therefore, it would take Alice's friend 5/6 of an hour (or 50 minutes) to complete the entire job on her own.