Question 865720
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/x + 1/y = 1/z}}}



{{{1/10 + 1/8 = 1/z}}}



{{{4/40 + 1/8 = 1/z}}}



{{{4/40 + 5/40 = 1/z}}}



{{{(4 + 5)/40 = 1/z}}}



{{{9/40 = 1/z}}}



{{{9z = 40*1}}}



{{{9z = 40}}}



{{{z = 40/9}}}



It will take them {{{40/9}}} hours to get the job done if they work together (Note: {{{40/9 = 4.4444}}} hours approximately)