blokker wrote:
Q: If five machines working at the same rate can do \(\frac{3}{4}\) of a job in 30 minutes, how many minutes would it take two machines working at the same rate to do \(\frac{3}{5}\) of the job?
(A) 45
(B) 60
(C) 75
(D) 80
(E) 100
Could someone help with this please? Thank you!
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Manhattan Prep sometimes uses the following formula for multiple workers:
Work = Number of Workers x Individual Rate x TimeAdd one extra column, Number of Workers, to the very straightforward RTW table.
Writing this method out makes it look hard. It isn't. And it's fast. It took me 41 seconds.
Simply manipulate the W = (
# * RATE * TIME) formula, just as if it were without the extra factor.
W = Work
# = # of workers
R = individual rate
T = timeSolving with rates and time in hours first. See top table.
"[F]ive machines working at the same rate can do \(\frac{3}{4}\) of a job in 30 minutes..." 30 minutes = \(\frac{1}{2}\)hour
1. We need an individual rate, which will be used to find time taken in Case 2.
Just from manipulating the formula:
individual Rate, R is \(\frac{W}{(# * T)}\)
2. Calculate denominator first: (# * T)
= 5 * \(\frac{1}{2}\) = \(\frac{5}{2}\)
3. Find individual rate --
\(\frac{W}{(# * T)}\)\(\frac{3}{4}\) ÷ \(\frac{5}{2}\) =
\(\frac{3}{4} * \frac{2}{5}\) =
\(\frac{3}{10}\) = Individual rate (amount of work per hour)
4. How much time will it take "two machines working at the same rate to do \(\frac{3}{5}\) of the job?"
T =
\(\frac{W}{(# * R)}\)Denominator first: 2 * \(\frac{3}{10}\) =
\(\frac{6}{10}\) = \(\frac{3}{5}\)
Find time: \(\frac{3}{5}\) ÷ \(\frac{3}{5}\) =
\(\frac{3}{5}\) * \(\frac{5}{3}\) = 1
1
hour =
60 minutesSolving with time and rates in minutes, see second table1. We need individual worker's rate, which will be used to calculate time in Case 2
\(\frac{W}{(# * T)}\) =
Individual Rate, R2. Calculate denominator first: (# * T) =
5 * 30 = 150
3. Find individual rate --
\(\frac{W}{(# * T)}\)\(\frac{3}{4}\) ÷ 150 = \(\frac{3}{4}\)* \(\frac{1}{150}\)= \(\frac{3}{600}\) =
\(\frac{1}{200}\) = Individual Rate in amount of work per minute
4. Find time for Case 2. "How many minutes would it take two machines working at the same rate to do \(\frac{3}{5}\) of the job?"
T =
\(\frac{W}{(# * R)}\)Denominator first: 2 * \(\frac{1}{200}\) = \(\frac{2}{200}\) = \(\frac{1}{100}\)
Time = \(\frac{3}{5}\) ÷ \(\frac{1}{100}\) =
\(\frac{3}{5}\) * \(\frac{100}{1}\) =
\(\frac{300}{5}\) = 60 minutes
Answer B
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