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help

ProMagma  Nov 3, 2017
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 #1
avatar+78755 
+1

Let the portion of the job that Alice can complete in one hr  = 1/ x

 

Let the portion of the job that Bob can complete in one hr  =1/ y

 

Let the portion of the job that Charlie can complete in one hr  = 1/ z

 

So  we have this system

 

2 [ 1/x + 1/y]  =  1    ⇒   1/x + 1/y  = 1/2    (1)

3 [ 1/x + 1/z ]  = 1    ⇒  1/x + 1/z  =  1/3  (2)

4[ 1/y + 1/z]  = 1    ⇒   1/z  + 1/y =  1/4    (3)

 

Subtract  (3)  from (1)     ⇒   1/x - 1/z  =  1/4   ( 4)

 

Add  (2)  + (4) =    2/x  =  7/12   ⇒   1/x =  7/24

 

Using (1)  to find y, we have that

 

 1/y  =  `1/2  - 7/24  =  5/24

 

And  using  (3)  to find 1/z  we have

 

1/z  =  1/4  - 5/24  =      6/24  - 5/24   =  1/24

 

So.....Alice completes 7/24 of the job in an hour......Bob completes 5/24  of the job in an hour  and Charlie completes 1/24  of the job in an hour

 

Add these  and take the reciprocal  =    [7 + 5  + 1 ] / 24  =   13/24

 

So.......they take  24/13 hrs  ≈ 1.846  hrs to complete the job working together

 

 

cool cool cool

CPhill  Nov 3, 2017
edited by CPhill  Nov 3, 2017
edited by CPhill  Nov 3, 2017
edited by CPhill  Nov 4, 2017
 #2
avatar+499 
0

Thanks that is a lot of work!! Ur da best!!

ProMagma  Nov 4, 2017

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