Step-by-step explanation:
Let the total work be x or you can take it as 1 since it won't matter
Let the time taken by Mary to finish the work alone be y.
So the rate at which Mary finishes the work alone is x/y . Here we are taking the rate because for both Mary and Carol the rate at which they are doing work will always remain constant.
Now we also know that Carol works twice as fast as Mary so Carol's rate of work is 2*(x/y). Here * means multiplication symbol.
So there total rate of work when working together is 2*(x/y) + ( x/y). This is equal to 3*(x/y). Call this equation 1.
And we know from the question that when they work together, they can finish the work in 4 hours. So the rate at which both of them work together is x/4. Call this equation 2
Ok so now we know that their combined rate of work is 3*(x/y) as from equation 1 and x/4 as from equation 2. Putting them together:-
3*(x/y) = x/4
Here we can cut off x on both sides as both are on the numerator side:-
3/y= 1/4
This means y=12
So Mary will take 12 hours to complete the work and Carol will take 6 hours to complete the work if they work alone.
The time it will take carol to do the job alone in terms of "x" is [tex]y=\frac{4x}{x-4}[/tex]
Let the time it will take Carol to finish the job alone be "y"
The time it took them to finish the job = 4 hours
To get the time it will take carol to do the same job alone, we can express it as a reciprocal;
[tex]\frac{1}{x} +\frac{1}{y} =\frac{1}{4}[/tex]
Find the LCM and find the value of "y"
[tex]\frac{y+x}{xy}= \frac{1}{4} \\4(y + x) = xy\\4y+4x=xy\\4x=xy-4y\\4x=y(x-4)\\[/tex]
Divide both sides by x-4
[tex]\frac{4x}{x-4} =\frac{y(x-4)}{x-4}\\ \frac{4x}{x-4} =ySwap\\y=\frac{4x}{x-4}[/tex]
Hence the time it will take carol to do the job alone in terms of "x" is [tex]y=\frac{4x}{x-4}[/tex]
Complete question:
If Mary can finish the job in x hours alone, how many hours will it take Carol to do the same job alone? if they can finish the project in 4hours
Learn more here: https: //brainly.com/question/23351459
