carcass wrote:
Each machine at a toy factory assembles a certain kind of toy at a constant rate of one toy every 3 minutes. If 40 percent of the machines at the factory are to be replaced by new machines that assemble this kind of toy at a constant rate of one toy every 2 minutes, what will be the percent increase in the number of toys assembled in one hour by all the machines at the factory, working at their constant rates?
A. 20
B. 25
C. 30
D. 40
E. 50
We have two rates and hence two different total number of toys produced: 100% of original machines at original rate, then 40% of machines at a new rate and 60% of machines at original rate
Assume 100 machines.
Change rates in minutes to rates in hours.
And assume time = 1 hour
Finally, 40% of 100 are new = 40 new machines and 60 old machines
Number of machines * R * T = Work
Rates in minutes --> rates in hours
Original rate:
\(\frac{1 toy}{3 mins} = \frac{20 toys}{60 mins}= \frac{20 toys}{1 hr}\) , = \(\frac{20}{1}\)
and
New rate FOR 40 MACHINES:
\(\frac{1 toy}{2 mins} =\frac{30 toys}{60 mins} = \frac{30 toys}{1 hr}\) = \(\frac{30}{1}\)
(1). Original number of toys produced
100 machines at the original rate of \(\frac{20}{1}\) produce (100 * \(\frac{20}{1}\)* 1) =
2,000 toys originally produced(2). Some old plus some new machines at different rates = new number of toys produced
So total toys produced now are made by 60 machines at original rate + 40 machines at new rate
Total toys that 60 machines produce: (60 * \(\frac{20}{1}\) * 1) = 1,200 toys
Total toys that 40 machines produce: (40 * \(\frac{30}{1}\) * 1) = 1,200 toys
1,200 + 1,200 =
2,400 total toys now produced(3). Percent change:
\(\frac{change}{original}\) x 100 :
\(\frac{400}{2000}\)* 100 = 20%
Answer A
_________________
The humblest praise most, while cranks & malcontents praise least. Praise almost seems to be inner health made audible. ~ C. S. Lewis