
Algebra PreAlgebra and Basic Algebra Math Forum 
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April 30th, 2017, 08:25 PM  #1 
Member Joined: Jan 2017 From: US Posts: 86 Thanks: 5  Solve For How Long It Would Take To Dig A Ditch Dave can dig a ditch in 6 hours, and Sam can dig a ditch in 4 hours. Frank can fill a ditch in 8 hours. If Dave and Sam dig a ditch while Frank tries to fill it. Solve for how long it will take to dig the ditch. Show all of your work and explain your solution. 
April 30th, 2017, 08:27 PM  #2 
Senior Member Joined: Feb 2016 From: Australia Posts: 1,230 Thanks: 424 Math Focus: Yet to find out. 
Sounds like dirty work. Care to do some for me first? 
April 30th, 2017, 08:29 PM  #3 
Senior Member Joined: Aug 2012 Posts: 1,414 Thanks: 342  
April 30th, 2017, 08:29 PM  #4 
Member Joined: Jan 2017 From: US Posts: 86 Thanks: 5 
Haha, but nope. I don't usually spend time answering questions on math forums (or... digging ditches) However, if you need help with something artsy, I'm your person! 
May 1st, 2017, 03:32 AM  #5 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 9,757 Thanks: 651  
May 1st, 2017, 10:57 AM  #6 
Member Joined: Feb 2015 From: Southwest Posts: 96 Thanks: 24 
Personally, I don't know why Sam and Dave don't take Frank out and finish quickly. Denis gave a great hint that I will add onto. If Dave can dig a ditch in six hours then his formula by himself to dig one ditch is $\displaystyle \frac{x}{6}=1$ ditch Same with Sam similarly. Frank on the other hand wants to take your ditch away, so his x would be negative, ie: $\displaystyle \frac{x}{8}=1$ The question asks how long does it take to dig one ditch, well Sam and Dave can combine efforts to shorten the time it takes to dig the ditch (additive) but Frank lengthens the time it takes (subtractive). Hopefully this helps you draft the formula and then solve for x. 
May 1st, 2017, 11:26 AM  #7 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 9,757 Thanks: 651  
May 3rd, 2017, 01:30 PM  #8 
Member Joined: Jan 2017 From: US Posts: 86 Thanks: 5 
I appreciate all of the hard mathematical work that is going on here, guys Lol


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