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 math-challenged individual. Thank you sooo much for your careful and complete explanation!

To find out how many hours it will take for William to finish his work alone, we need to determine his individual work rate.

Let's assume that the rate at which Andy completes his work is A toys per hour, and the rate at which William completes his work is W toys per hour.

From the given information, we know that:
- When William and Andy work together, it takes them 4 hours to complete the work, so their combined work rate is 1/4 toys per hour. This can be expressed as 1/4 = A + W.
- When William works alone, it takes him 5 hours to complete the work, so his individual work rate is 1/5 toys per hour. This can be expressed as 1/5 = W.
- When Andy works alone, it takes him 2 hours to complete the work, so his individual work rate is 1/2 toys per hour. This can be expressed as 1/2 = A.

Solving these equations simultaneously, we can substitute the value of A from the second equation (1/2) into the first equation:
1/4 = (1/2) + W
1/4 - 1/2 = W
2 - 1/2 = W
1/2 = W

Therefore, we have determined that William's individual work rate is 1/2 toys per hour. This means that it will take him 2 hours to complete his work alone.