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๐˜›๐˜ธ๐˜ฐ ๐˜ญ๐˜ข๐˜ณ๐˜จ๐˜ฆ ๐˜ข๐˜ฏ๐˜ฅ 1 ๐˜ด๐˜ฎ๐˜ข๐˜ญ๐˜ญ ๐˜ฑ๐˜ถ๐˜ฎ๐˜ฑ๐˜ด ๐˜ค๐˜ข๐˜ฏ ๐˜ง๐˜ช๐˜ญ๐˜ญ ๐˜ข ๐˜ด๐˜ธ๐˜ช๐˜ฎ๐˜ฎ๐˜ช๐˜ฏ๐˜จ ๐˜ฑ๐˜ฐ๐˜ฐ๐˜ญ ๐˜ช๐˜ฏ 4 ๐˜ฉ๐˜ฐ๐˜ถ๐˜ณ๐˜ด. ๐˜–๐˜ฏ๐˜ฆ ๐˜ญ๐˜ข๐˜ณ๐˜จ๐˜ฆ ๐˜ข๐˜ฏ๐˜ฅ 3 ๐˜ด๐˜ฎ๐˜ข๐˜ญ๐˜ญ ๐˜ฑ๐˜ถ๐˜ฎ๐˜ฑ๐˜ด ๐˜ค๐˜ข๐˜ฏ ๐˜ข๐˜ญ๐˜ด๐˜ฐ ๐˜ง๐˜ช๐˜ญ๐˜ญ ๐˜ต๐˜ฉ๐˜ฆ ๐˜ด๐˜ข๐˜ฎ๐˜ฆ ๐˜ด๐˜ธ๐˜ช๐˜ฎ๐˜ฎ๐˜ช๐˜ฏ๐˜จ ๐˜ฑ๐˜ฐ๐˜ฐ๐˜ญ ๐˜ช๐˜ฏ 4 ๐˜ฉ๐˜ฐ๐˜ถ๐˜ณ๐˜ด. ๐˜๐˜ฐ๐˜ธ ๐˜ฎ๐˜ข๐˜ฏ๐˜บ ๐˜ฉ๐˜ฐ๐˜ถ๐˜ณ๐˜ด ๐˜ธ๐˜ช๐˜ญ๐˜ญ ๐˜ช๐˜ต ๐˜ต๐˜ข๐˜ฌ๐˜ฆ 4 ๐˜ญ๐˜ข๐˜ณ๐˜จ๐˜ฆ ๐˜ข๐˜ฏ๐˜ฅ 4 ๐˜ด๐˜ฎ๐˜ข๐˜ญ๐˜ญ ๐˜ฑ๐˜ถ๐˜ฎ๐˜ฑ๐˜ด ๐˜ต๐˜ฐ ๐˜ง๐˜ช๐˜ญ๐˜ญ ๐˜ต๐˜ฉ๐˜ฆ ๐˜ด๐˜ธ๐˜ช๐˜ฎ๐˜ฎ๐˜ช๐˜ฏ๐˜จ ๐˜ฑ๐˜ฐ๐˜ฐ๐˜ญ.(๐˜ž๐˜ฆ ๐˜ข๐˜ด๐˜ด๐˜ถ๐˜ฎ๐˜ฆ ๐˜ต๐˜ฉ๐˜ข๐˜ต ๐˜ข๐˜ญ๐˜ญ ๐˜ญ๐˜ข๐˜ณ๐˜จ๐˜ฆ ๐˜ฑ๐˜ถ๐˜ฎ๐˜ฑ๐˜ด ๐˜ข๐˜ณ๐˜ฆ ๐˜ด๐˜ช๐˜ฎ๐˜ช๐˜ญ๐˜ข๐˜ณ ๐˜ข๐˜ฏ๐˜ฅ ๐˜ข๐˜ญ๐˜ญ ๐˜ด๐˜ฎ๐˜ข๐˜ญ๐˜ญ ๐˜ฑ๐˜ถ๐˜ฎ๐˜ฑ๐˜ด ๐˜ข๐˜ณ๐˜ฆ ๐˜ข๐˜ญ๐˜ด๐˜ฐ ๐˜ด๐˜ช๐˜ฎ๐˜ช๐˜ญ๐˜ข๐˜ณ.)

 May 20, 2020
 #1
avatar+732 
+2

Hi Strawberrymilk.tae!

 

I think the question has already been answered here: https://web2.0calc.com/questions/math_71247

 

:)

 May 21, 2020
 #2
avatar
-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   โ†’   8/R  + 4/r  = 1

1*(1/R)*4 + 3*(1/r)*4   = 1   โ†’   4/R + 12/r  = 1

 

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

 

-20/r  = -1   โ†’   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
avatar+732 
+1

hi Guest!

 

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

lokiisnotdead  May 21, 2020

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