math word problem
posted by M.A. .
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?
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
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 math-challenged individual. Thank you sooo much for your careful and complete explanation!