Question 864355
x = time it takes for person A to do the job alone
y = time it takes for person B to do the job alone
z = time it takes for them to get the job done when they work together



When we make those definitions above, it turns out that we can tie x,y,z together with this equation 


{{{1/x + 1/y = 1/z}}}



In this case, 



x = 10
y = unknown (leave it as y for now)
z = 7



Plug those into the equation and solve for y



{{{1/x + 1/y = 1/z}}}



{{{1/10 + 1/y = 1/7}}}



{{{1/y = 1/7-1/10}}}



{{{1/y = 10/70-1/10}}}



{{{1/y = 10/70-7/70}}}



{{{1/y = (10-7)/70}}}



{{{1/y = 3/70}}}



{{{1*70 = 3y}}}



{{{70 = 3y}}}



{{{70/3 = y}}}



{{{y = 70/3}}}



So it will take {{{highlight(70/3)}}} hours for the second person to do the job alone.



Since {{{70/3 = 23 & 1/3}}}, this means it takes {{{highlight(23&1/3)}}} hours ({{{highlight(23&1/3)}}} hours = <font color="red">23 hours, 20 minutes</font>)



If you want the time in minutes only, then multiply it by 60 to get {{{(70/3)*60 = 4200/3 = 1400}}} minutes