Hadrienlbb wrote:

A manager hired 4 employees to complete a certain project in 15 days. After 10 days of work the employees completed only half of the project. How many additional employees should the manager hire to finish this project in time if each employee works at the same constant rate?

A) 1

B) 2

C) 3

D) 4

E) 5

ALTER THE STANDARD RT=W FORMULA A BIT

Add (# of workers) to the standard formula (R*T=W).

That is, write it as (#)*R*T=W, or W=(#)*R*T. Manipulate that formula in the same way as RT=W

FIRST PHASE OF WORK - find individual rate. From that you can find # of workers for the second phase.

W = (# of workers) * r * tW = \(\frac{1}{2}\)

# of workers = 4

r = ??

Time = 10 days

W = (#)*r*t

\(\frac{1}{2} = 4 * r * 10\)

\(r = \frac{(\frac{1}{2})}{4*10}=\frac{(\frac{1}{2})}{40}=\frac{1}{80}\)

At that individual rate, how many [more] workers are needed to finish the project on time? There are (15 - 10) = 5 days left.

SECOND PHASE - use individual rate to find # of workers needed

W = (# of workers) * r * tW = \(\frac{1}{2}\)

# of workers = N = ??

r = \(\frac{1}{80}\)

t = 5 days

W = (#)*r*t

\(\frac{1}{2}= N * \frac{1}{80} * 5\)

\(N =\frac{(\frac{1}{2})}{(\frac{1}{80}*5)}=\frac{(\frac{1}{2})}{(\frac{1}{16})}=\frac{1}{2}*16 = 8\)

(# of workers, N) needed to finish = 8

There are already 4 workers. He needs 4 more.

Answer D

P.S. - I don't use N. I use #, to remind myself what I'm after; "N" isn't as clear. I use N here because formatting goes berserk with the # sign.
_________________

In the depths of winter, I finally learned

that within me there lay an invincible summer.

-- Albert Camus, "Return to Tipasa"