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# 𝐻𝑒𝓁𝓅 𝓂𝑒!

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𝘛𝘸𝘰 𝘭𝘢𝘳𝘨𝘦 𝘢𝘯𝘥 1 𝘴𝘮𝘢𝘭𝘭 𝘱𝘶𝘮𝘱𝘴 𝘤𝘢𝘯 𝘧𝘪𝘭𝘭 𝘢 𝘴𝘸𝘪𝘮𝘮𝘪𝘯𝘨 𝘱𝘰𝘰𝘭 𝘪𝘯 4 𝘩𝘰𝘶𝘳𝘴. 𝘖𝘯𝘦 𝘭𝘢𝘳𝘨𝘦 𝘢𝘯𝘥 3 𝘴𝘮𝘢𝘭𝘭 𝘱𝘶𝘮𝘱𝘴 𝘤𝘢𝘯 𝘢𝘭𝘴𝘰 𝘧𝘪𝘭𝘭 𝘵𝘩𝘦 𝘴𝘢𝘮𝘦 𝘴𝘸𝘪𝘮𝘮𝘪𝘯𝘨 𝘱𝘰𝘰𝘭 𝘪𝘯 4 𝘩𝘰𝘶𝘳𝘴. 𝘏𝘰𝘸 𝘮𝘢𝘯𝘺 𝘩𝘰𝘶𝘳𝘴 𝘸𝘪𝘭𝘭 𝘪𝘵 𝘵𝘢𝘬𝘦 4 𝘭𝘢𝘳𝘨𝘦 𝘢𝘯𝘥 4 𝘴𝘮𝘢𝘭𝘭 𝘱𝘶𝘮𝘱𝘴 𝘵𝘰 𝘧𝘪𝘭𝘭 𝘵𝘩𝘦 𝘴𝘸𝘪𝘮𝘮𝘪𝘯𝘨 𝘱𝘰𝘰𝘭.(𝘞𝘦 𝘢𝘴𝘴𝘶𝘮𝘦 𝘵𝘩𝘢𝘵 𝘢𝘭𝘭 𝘭𝘢𝘳𝘨𝘦 𝘱𝘶𝘮𝘱𝘴 𝘢𝘳𝘦 𝘴𝘪𝘮𝘪𝘭𝘢𝘳 𝘢𝘯𝘥 𝘢𝘭𝘭 𝘴𝘮𝘢𝘭𝘭 𝘱𝘶𝘮𝘱𝘴 𝘢𝘳𝘦 𝘢𝘭𝘴𝘰 𝘴𝘪𝘮𝘪𝘭𝘢𝘳.)

May 20, 2020

#1
+2

Hi Strawberrymilk.tae!

:)

May 21, 2020
#2
-2

Call the portion of the job that the large pump can do in 1 hour  = 1/R   where R is the total number of hours that it takes 1 large pump to complete the task

Call the portion of the job that the small pump can do in 1 hour = 1 / r   where r is the total number of hours that it takes 1 small pump to complete the task

And Rate x Time =  Amt of the job done

So...we have the following system

2*(1/R)*4  + 1*(1/r)*4  = 1   →   8/R  + 4/r  = 1

1*(1/R)*4 + 3*(1/r)*4   = 1   →   4/R + 12/r  = 1

Multiply the second equation by -2 and add it to the first

-20/r  = -1   →   r/20  = 1    so r = 20   hours for one small pump to fill  the pool

And using     8/R + 4/r = 1  to solve for R, we have

8/R + 4/20  = 1

8/R + 1/5  = 1

8/R = 4/5

R/8  = 5/4

R = 40/4  = 10 hrs for one large pump to fill the  pool

So... for 4 large pumps and 4 small pumps working in unison, we have.....

The 4 large pumps will fill  4/10  = 2/5 of the pool in one hour  [each fills 1/10 of the pool in one hour]

The 4 small pumps will fill  4/20  = 1/5  of the pool in one hour  [each fills 1/20 of the pool in  one hour]

So...in one hour    2/5 + 1/5 = 3/5  of the pool is filled

And...inverting this fraction gives us the total time = 5/3 hrs =  1 + 2/3 hrs =  1 hr 40 min

May 21, 2020
#3
+1

hi Guest!

I think your solution was just CPhill's but copied and pasted... make sure you give him credit next time :)