Habiba and Halima together can do a work in 20-days. They were
working together, but after 6 days Habia went away. Halima finished
the rest of the work in 21 days. How many days would Halima need to
complete the whole work?
in days after beginning the work,
Answers
Combined rate = 1/20 or .05 works/day
Partial work = 6(.05) = .30 complete
Halima completed .70 of the work in 21 days
Halima's work rate = 21/.70 or 30 days/work
10
msbpr's avatar
msbpr
7 years ago
I think this is how is goes...quite involved.
Let x= time Habia could do the job alone
let y= time Halima could do the job alone.
20 = time they would need doing it together. (each on the job equally)
Basically the Work equation would be:
20/x + 20/y = 1
This is the basic formula for doing 1 complete job.
But, there is a split in the time, so, now look at this one.
6/x + 27/y = 1
See how 6 represents the time Habia put in and 27 hrs. represents the time Halima put in?
So you have 2 equations now:
"flattening" them out--is often easier,
they become:
20y + 20x = xy
and
6y + 27x = xy
Do you get this multiplication step to eliminate denominators?
Now, subtract the second one from the first and you should get a simple
equation of 14y-7x=0 Can you get this?
Solve for x and then go back to 20/x + 20/y =1 from the very beginning and put your value in for x....so you have an equation only in y now.
Flatten it or do whatever you do in your class and you should get the answer for
y which is 30....and then x falls out...
NOTE:
The fact that the equations subtract so smoothly and the answers come out whole numbers is a pretty good sign that you are right.
Good luck..
The answers I got were Habia 60 and Halima 30.
This is a tough problem....
Step-by-step explanation: