# Need help with "work" problem

#### max

##### Junior Member
If x people working at the same rate can complete a job in h hours, what part of the same job can one person working alone complete in k hours?

I havn't seen a work problem like this before.

Can anyone help?

#### Subhotosh Khan

##### Super Moderator
Staff member
If x people working at the same rate can complete a job in h hours, what part of the same job can one person working alone complete in k hours?
So

1 person - in h hours - can complete 1/x part of the job

1 person - in 1 hours - can complete 1/(xh) part of the job

Now finish it....

#### max

##### Junior Member
Then the answer would be k/xh

I don't understand the 1/x part. How u do that?

I get the 1 over h part. It would be the same if I said Jack can paint a room in 3 hours that would mean he could paint 1/3 of the room in 1 hour.

I don't get the first part 1/x. What does that mean?

thanks a bunch!

#### Denis

##### Senior Member
1/x times h is same as h/x

#### max

##### Junior Member
I think I got it now. I made up a problem using that solving approach. Is my answer right?

If 3 friends can makeover and paint the garage in 3 hours, how long would it take just one of them to do it if the others changed their minds about doing it?

So if 3 can do it in 3 hours
1 can do 1/3 of it in 3 hours
and can do 1/3*3, or 1/9 of it in 1hour
So he can do the whole job in 9 hours.

Is that right?

#### Subhotosh Khan

##### Super Moderator
Staff member
If two (2) people can finish a job - how much each(1) do = 1/2

If two (3) people can finish a job - how much each(1) do = 1/3

If two (4) people can finish a job - how much each(1) do = 1/4

If two (x) people can finish a job - how much each(1) do = 1/x

#### Subhotosh Khan

##### Super Moderator
Staff member
If 3 friends can makeover and paint the garage in 3 hours, how long would it take just one of them to do it if the others changed their minds about doing it?

So if 3 can do it in 3 hours
1 can do 1/3 of it in 3 hours
and can do 1/3*3, or 1/9 of it in 1hour
So he can do the whole job in 9 hours.

Is that right?... CORRECT