Question 1155509
If the times for each of them working alone were a, b, c
then, skipping steps,
{{{1/a+1/b+1/c=13/24}}}, the rate


The time for all three working together,  {{{24/13}}} hours


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{{{system(1/a+1/b=1/2,1/a+1/c=1/3,1/b+1/c=1/4)}}}


{{{2/a+2/b+2/c=1/2+1/3+1/4=13/12}}}


{{{1/a+1/b+1/c=13/24}}}{{{just}}}{{{the}}}{{{total}}}{{{rate}}}