My Math Forum Solve For How Long It Would Take To Dig A Ditch

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 April 30th, 2017, 09:25 PM #1 Senior Member   Joined: Jan 2017 From: US Posts: 104 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, 09:27 PM #2 Senior Member   Joined: Feb 2016 From: Australia Posts: 1,475 Thanks: 494 Math Focus: Yet to find out. Sounds like dirty work. Care to do some for me first? Thanks from Indigo28
 April 30th, 2017, 09:29 PM #3 Senior Member   Joined: Aug 2012 Posts: 1,679 Thanks: 436 Thanks from romsek
 April 30th, 2017, 09:29 PM #4 Senior Member   Joined: Jan 2017 From: US Posts: 104 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, 04:32 AM   #5
Math Team

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Quote:
 Originally Posted by Indigo28 Dave can dig a ditch in 6 hours Sam can dig a ditch in 4 hours Frank can fill a ditch in 8 hours
Hint: what's the situation after 1 hour? Dig?

 May 1st, 2017, 11:57 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. Thanks from Indigo28
 May 1st, 2017, 12:26 PM #7 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 11,370 Thanks: 730 Thanks from romsek
 May 3rd, 2017, 02:30 PM #8 Senior Member   Joined: Jan 2017 From: US Posts: 104 Thanks: 5 I appreciate all of the hard mathematical work that is going on here, guys Lol

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