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# help. Thank You!

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help

ProMagma  Nov 3, 2017
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#1
+82813
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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

CPhill  Nov 3, 2017
edited by CPhill  Nov 3, 2017
edited by CPhill  Nov 3, 2017
edited by CPhill  Nov 4, 2017
#2
+549
0

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

ProMagma  Nov 4, 2017

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