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avatar+1786 

I'm trying to figure out this new formula. Can anybody show me how's it done?

 Feb 2, 2019
 #1
avatar+98153 
+2

1)     Note that  we have this

 

1/Alaina's time  +  1/Aliya's time  =  1/Time for both to do the job

Let's fill in what we know

 

1/8  +  1/Aliya's Time  =  1/5       subtract  1/8  from both side

 

1/Aliya's Time  =   1/5 - 1/8

 

1/Aliya's Time   =   8/40 - 5/40

 

1/Aliya's Time =  3/40     (1)

 

Note  one thihg......  that   if    3/4 = 9/12      then it is also true that   4/3 = 12/9

 

So....this implies that (1)  can be written as

 

Aliya"s Time / 1  =  40/3

 

Aliya's Time =  40/3  hrs  =  13.3  hrs. to do the job by herself  !!!

 

 

cool cool cool

 Feb 2, 2019
 #2
avatar+98153 
+2

(2)  Got to be careful here.....we want everything in hours....so

80min/ 60min = 4/3 hrs

 

So.....we have this equation

 

1/2 + 1 / (4/3)  = 1/ Time for both to do the job

 

Note 1 /( 4/3)   = 3/4

 

So we have

 

1/2 +   3/4  =  1 /Time for both to do the job

 

2/4 + 3/4  = 1 /Time for both to do the job

 

5/4  = 1 /Time for both to do the job    

 

And using our "trick" from the previous problem we can write

 

4/5  = Time for both to do the job   = 4/5 hours   =  .8hrs        (.8 *60 = 48 min )

 

 

We can check this

Note that  since it takes you 120 min to complete the job.... each minute you complete 1/120 of the job

And your friend completes (1/80) of the job in one minute

 

So.....

 

Time you work * (1/120)  + time your friend works (1/80)  =

 

48(1/120) + 48(1/80) = 

 

48/120  + 48/180  =  1 (whole job done)

 

 

 

cool cool cool

 Feb 2, 2019
 #3
avatar+98153 
+2

Note one other thing.....when we know the rate for each person....it is easy to solve these

 

For example....you do a job in 10 hrs and your friend does it in 8 hrs

 

We have

 

1/8 + 1/10

 

5 / 40  + 4/40 =   9/40

 

"Flip" this fraction  = 40/9  = 4.44 hrs =   time for both of you to do the job together !!!

 

 

cool cool cool

 Feb 2, 2019
 #4
avatar+1786 
+1

Thanks for the help CPhill! This all makes sense now for this new formula.

 

--7H3_5H4D0W

GAMEMASTERX40  Feb 2, 2019

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