Increasing the number of workers reduces the number of days

[zak100]

Homework Statement

If 15 workers can pave 18 driveways in 24 days, how many days would it take 40 workers to pave 22 driveways?

Homework Equations

Set of worker * driveways* days/Another set of workers * driveways

The Attempt at a Solution

15 * 18 *24/40 * 22 =54/11 wrong

Some body please guide. I don't know the method for solving such problems. I don't know the usage of two set of data.
Zulfi.[/B]

 

[Doc Al]

The "trick" is that the number of driveways per day per worker is a constant:

(#driveways)/[(#workers)*(#days)] = constant

So set up an equation comparing that expression (on the left) for the first set of data (15 workers, etc.) to one for the second set of data (40 workers, etc.). The only unknown will be the #days in the second set. Solve!

 

[Ray Vickson]

Homework Statement

If 15 workers can pave 18 driveways in 24 days, how many days would it take 40 workers to pave 22 driveways?

Homework Equations

Set of worker * driveways* days/Another set of workers * driveways

The Attempt at a Solution

15 * 18 *24/40 * 22 =54/11 wrong

Some body please guide. I don't know the method for solving such problems. I don't know the usage of two set of data.
Zulfi.[/B]

Do not just write down numbers without thinking. You need to approach such problems systematically.

For example, how long would it take 1 worker to pave 18 driveways? From that, how long would it take 1 worker to pave 1 driveway? Now continue from that.

 

[zak100]

Hi,
Did you mean:
15/(18 * 24) = 40/(20 * Days)

Still the answer is not correct.
I know that: if we increase the labors less days would be required to construct a drive way. So from 15 workers to 40 workers 2 days reqd for a driveway.
15*24/40 = 9 days required for a drive way.

Zulfi.

 

[Doc Al]

15/(18 * 24) = 40/(20 * Days)

The left hand side makes sense. How did you get the right hand side?

Both sides must have this form:

(#driveways)/[(#workers)*(#days)]

 

[zak100]

Hi,
Thanks. I got the answer.
First part (LHS): # of driveways = 18
#of workers = 15
# of days =24
Second part(RHS):
#of drive ways = 22
#of days = ?
#of workers=40
(#driveways)/[(#workers)*(#days)] of First part= (#driveways)/[(#workers)*(#days)] of Second part
Putting values:
18/(15 * 24) = 22/(40* days)
days = 11

Thanks.

Zulfi.