Problem on beats homework problem

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The problem involves a man drumming in front of a mountain, where the echo becomes indistinct at certain drumming rates. Initially, the echo is not heard at 40 beats per minute, and after moving 90 meters closer, it is not heard at 60 beats per minute. The key to solving the problem lies in understanding that the echo will not be heard when the time for sound to travel to the mountain and back matches the interval between drum beats. To find the distance from the mountain to the man's original position and the velocity of sound, one must set up equations based on the given rates and distances. This problem requires applying concepts of sound travel time and frequency.
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problem on beats , pleaseeee helppppp!

I am puzzled!
problem----- A man standing in front of a mountain beats a drum at regular intervals. The drumming rate is gradually increased and he finds that the echo is not heard distinctly when the rate becomes 40 per minute. He moves nearer to the mountain by 90 meters and finds that the echo is again not heard when drumming rate becomes 60 per minute. Calculate
(a) the distance between the mountain and initial position of the man , and
(b) the velocity of the sound.

I am desperate for helpppppp.
 
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The echo beat will not be heard when the time for sound to travel to the cliff and back equals the time between beats.
 
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Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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