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
first of all. the question is ambiguous from the start. is 45 min the rate they work both together? or each independently?
I suppose together...
so
\(\frac{1}{M}+\frac{1}{P}=\frac{1}{45}\)
then
we are told:
\(\frac{2}{M}+\frac{1}{M}=\frac{1}{20}\)
we can find the rate for M:
\(\frac{1}{60}\) -> so M needs 60 min to finish the job.
now, we are given \(\frac{1}{M}\), we can find \(\frac{1}{P}\)
\(\frac{1}{60}+\frac{1}{P}=\frac{1}{45}\)
\(\frac{1}{P}=\frac{1}{180}\)
So M needs 180 mins, or 3hours to complete the job alone.