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Question 207194: it takes you 8 hours to dig a hole, you and your brother dig a same size hole and it takes you 5 hours, how long will it take your brother to dig that same hole?
Found 2 solutions by Alan3354, mickclns:
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! it takes you 8 hours to dig a hole, you and your brother dig a same size hole and it takes you 5 hours, how long will it take your brother to dig that same hole?
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This type of problem required the sum of reciprocals approach.
I dig 1/8 of the hole per hour.
Bro digs 1/5 of the hole per hour.
Now you can add those.
Together, we dig 1/8 + 1/5 per hour
= 13/40 of the hole per hour.
--> 40/13 hours to dig the hole
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There's a shortcut, which is handy on a timed test, product/sum.
5*8/(5+8) = 40/13
Answer by mickclns(59)  (Show Source):
You can put this solution on YOUR website! 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  (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  (holes per hour). The amount you can dig in an hour is of a hole, and the amount he can dig in an hour is 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  . So, we need to solve the equation for your working together, A = RT or
 multiplying both sides by 8B
 distributing 5
 subtracting 5B from both sides
 dividing both sides by 3
 or 13 and 1/3 hours (the slacker!) and that is your answer.
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