Rock750 wrote:
Two musicians, Maria and Perry, work at independent constant rates to tune a warehouse full of instruments. If both musicians start at the same time and work at their normal rates, they will complete the job in 45 minutes. However, if Perry were to work at twice Maria’s rate, they would take only 20 minutes. How long would it take Perry, working alone at his normal rate, to tune the warehouse full of instruments?
A. 1 hr 20 min
B. 1 hr 45 min
C. 2 hr
D. 2 hr 20 min
E. 3 hr
One option is to
assign a "nice" value to the total job.
Since the Least Common Multiple of 45 and 20 is 180, let's say that there are
180 instruments in the warehouse.
Let M = the number of instruments that Maria can tune PER MINUTE
Let P = the number of instruments that Perry can tune PER MINUTE
Both musicians working TOGETHER complete the job in 45 minutes180/45 = 4
So, working TOGETHER, they can tune 4 instruments PER MINUTE
In other words, (Mary's rate) + (Perry's rate) = 4
We can write:
M + P = 4If Perry were to work at twice Mariaâ€™s rate, they would take only 20 minutes.180/20 = 9
So, in this scenario, they can tune 9 instruments PER MINUTE
In other words, (Mary's rate) + (Perry's rate) = 9
In this scenario, Perry's rate = 2M
So, we can write: M + 2M = 9
Simplify: 3M = 9
So, M = 3 (Maria can tune 3 instruments per minute)
Now that we know the value of M, we can use the equation
M + P = 4 to conclude that P = 1
In other words, Perry can tune 1 instrument per minute
If there are
180 instruments to tune, it will take Perry 180 minutes to complete the job.
Answer: E
Cheers,
Brent
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