document.write( "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? \n" ); document.write( "

Algebra.Com's Answer #156657 by mickclns(59) $\"\"$ $\"About$

You can put this solution on YOUR website!
No time at all ... you already dug it! But, seriously, folks:\r
\n" ); document.write( "\n" ); document.write( "The way it is written, it is very confusing, but I am assuming you mean:
\n" ); document.write( "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?\r
\n" ); document.write( "\n" ); document.write( "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 $\"1%2F8\"$ (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 $\"1%2FB\"$ (holes per hour). The amount you can dig in an hour is $\"1%2F8\"$ of a hole, and the amount he can dig in an hour is $\"1%2FB\"$ 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 $\"1%2F8+%2B+1%2FB=%28B%2B8%29%2F8B\"$ . So, we need to solve the equation for your working together, A = RT or
\n" ); document.write( " $\"1=%28%28B%2B8%29%2F8B%29+5\"$ multiplying both sides by 8B
\n" ); document.write( " $\"8B+=+5%28B%2B8%29\"$ distributing 5
\n" ); document.write( " $\"8B+=+5B+%2B+40\"$ subtracting 5B from both sides
\n" ); document.write( " $\"3B+=+40\"$ dividing both sides by 3
\n" ); document.write( " $\"B+=+40%2F3\"$ or 13 and 1/3 hours (the slacker!) and that is your answer. \n" ); document.write( "

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