mangamma wrote:
If 18 identical machines required 40 days to complete a job, how many fewer days would have been required to do the job if 54 additional machines of the same type had been used since the beginning?
A. 10 days
B. 40/3 days
C. 16 days
D. 80/3 days
E. 30 days
Potential traps: the question asks about
additional machines and how many
fewer days.
Just change the traditional
(R * T) = W formula.
Add one more variable,
# of machines, to the left hand side, this way
(# of machines * R * T) = WManipulate that formula in the same way that the "regular" RT=W gets manipulated
•
Step 1: Find the rate of an individual machine
# of machines = 18
R = ??
T = 40
W = 1
# of machines * R * T = W\(18 * R * 40 = 1\)
\(R = \frac{1}{18*40} = \frac{1}{720}\)•
Step 2: Use that individual machine rate to find the time that
54
additional machines would have needed to finish the work
# of machines = (18 + 54) = 72
R = \(\frac{1}{720}\)
T = ??
W = 1
# of machines * R * T = W\(72 * \frac{1}{720} * T = 1\)
\(T * \frac{72}{720} = 1\)
\(T = \frac{720}{72} = 10\) days 72 machines (i.e., 54 additional machines) would have required 10 days to finish the work.
•
Step 3: How many fewer days would have been required?
-- 18 machines required 40 days.
-- 72 machines would have required 30 days.
(40 - 30) = 10 days
Answer E