SOLUTION: It takes Jimmy ten hours to dig a 10 ft by 10 ft hole. Julia can dig the same hole in eight hours. Find how long it would take them if they worked together.

Algebra ->  Rate-of-work-word-problems -> SOLUTION: It takes Jimmy ten hours to dig a 10 ft by 10 ft hole. Julia can dig the same hole in eight hours. Find how long it would take them if they worked together.      Log On


   

Question 865720: It takes Jimmy ten hours to dig a 10 ft by 10 ft hole. Julia can dig the same hole in eight hours. Find how long it would take them if they worked together.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Note: the "10 ft by 10 ft" portion is irrelevant. It's put in there to throw you off. So ignore it. I would rephrase the statement to be "it takes Jimmy 10 hours to dig a single hole". And then maybe add on "Julia can dig the same hole, of the same volume and size, in 8 hours"

Let,
x = time it takes Jimmy to do the job alone
y = time it takes Julia to do the job alone
z = time it takes for them to get the job done when they work together


So that means,
x = 10
y = 8
z = unknown (we leave it as 'z' for now). We are solving for this and isolating this variable


1%2Fx+%2B+1%2Fy+=+1%2Fz


1%2F10+%2B+1%2F8+=+1%2Fz


4%2F40+%2B+1%2F8+=+1%2Fz


4%2F40+%2B+5%2F40+=+1%2Fz


%284+%2B+5%29%2F40+=+1%2Fz


9%2F40+=+1%2Fz


9z+=+40%2A1


9z+=+40


z+=+40%2F9


It will take them 40%2F9 hours to get the job done if they work together (Note: 40%2F9+=+4.4444 hours approximately)