Figuring out how long it takes to do a job (math problem)

Question

Q: Person E can do a job in 5 hours. Person E and person L can do the same job together in 2 hours. How long would it take person L to do the job alone?

I got 3 and 1/3 hours, but I am not sure if that is correct. Any help is appreciated!

Answer 1

Shared work problems like this are always, in essence, addition of fractions.

In this case E can do one job per 5 hours. This rate can be represented as

1 job/5hours or 1/5 job per hour.

L's rate we don't know, so L can perform 1 job per X hours.

Together E and L can perform one job per 2 hours, or 1 job/2hours

So your equation amounts to L's rate + E's rate = the total rate, or

1/5 + 1/x = 1/2

Solve for x by multiplying the entire equation by the common denominator 10x

This gives us 2x + 10 = 5x

and 10 = 3x

10/3 = x

Therefore L can do the job in 10/3 or 3 1/3 hours or 3 hours and 20 minutes.

Best wishes!

Answer 2

Stratton

You are correct ! Here is the justification if you need it.

Let's say the job is 100 units of work (this number doesn't matter but I have just chosen it as it is divisible by 5 and 2).

E can do the job in 5 hours. So he/she does 100/5 = 20 units of work per hour.

E and L together do the job in 2 hours. So together they must do 100 / 2 = 50 units of work per hour.

We know E can do 20 units of work per hour alone. So that means L does 30 units of work per hour alone.

So if L was working alone, would take 100 / 30 = 3 1/3 hours.

You are correct !

Well done.

Mike