Working Together Problems:

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  !!!

(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)

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 !!!