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

GAMEMASTERX40 Feb 2, 2019

#1**+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 !!!

CPhill Feb 2, 2019

#2**+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)

CPhill Feb 2, 2019

#3**+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 !!!

CPhill Feb 2, 2019

#4**-4 **

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

--7H3_5H4D0W

GAMEMASTERX40
Feb 2, 2019