math word problem
posted by M.A. on .
Andy and William work together to build a toy house. It will take William 5 hours and Andy 4 hours, or William 10 hours and Andy 2 hours to finish their work. If William works alone, how many hours will it take to finish his work?
5
10
15
20
Explain how you arrived at the answer.

There are two ways to do this, as a logic problem or as an algebra problem
If it will take William 5 hours and Andy 4 hours, or William 10 hours and Andy 2 hours to finish their work, then each decrease in time by Andy of 2 hours results in 5 more hours of work by William. So if Andy's work goes to zero then there will be 5 more hours of work required by William, so
10h + 5 h = 15 h.
By algebra if we say that the rate of work by William is x and that by Andy is y then
5x+4y=T Total task .....1
10x+2y=T
or
20x+4y=2T ..............2
subtract 1 from 2
15x=T, so it takes William 15 h 
Thank you Dr. Russ. I am so thrilled with your answer. It is the first time I have had an answer that I can truly understand and comprehend, being a mathchallenged individual. Thank you sooo much for your careful and complete explanation!