Question 207194
No time at all ... you already dug it!  But, seriously, folks:

The way it is written, it is very confusing, but I am assuming you mean:
It takes you 8 hours to dig a hole.  It takes you and your brother TOGETHER 5 hours to dig a same size hole.  How long will it take your brother to dig a same-sized hole alone?

So this is a variation of D = RT (distance = rate times time), or R = D/T-- in this case, A=RT or R=A/T where A is amount.  We don't know how big the hole is, but we don't need it. A = 1, where 1 represents 1 regulation-sized hole.  When dealing with yourself alone your rate is {{{1/8}}} (holes per hour).  Let B = the number of hours it would take your brother to dig this size hole (this the answer to the question).  So your brother's rate alone is {{{1/B}}} (holes per hour).  The amount you can dig in an hour is {{{1/8}}} of a hole, and the amount he can dig in an hour is {{{1/B}}} of a hole.  The amount you and your brother together can dig in an hour is just the sum of the amounts each of you can dig, that is {{{1/8 + 1/B=(B+8)/8B}}}.  So, we need to solve the equation for your working together, A = RT or 
{{{1=((B+8)/8B) 5}}}   multiplying both sides by 8B
{{{8B = 5(B+8)}}}    distributing 5
{{{8B = 5B + 40}}}   subtracting 5B from both sides
{{{3B = 40}}}   dividing both sides by 3
{{{B = 40/3}}} or 13 and 1/3 hours (the slacker!) and that is your answer.