On my Algebra II quiz today, I had a problem like this:

If it takes 10 workers 12 hours to build a building and it takes 20 workers 6 hours, how many hours will it take for 15 workers?

I thought the correct answer was 9 hours since 10 is half of 20, and 15 is right in the middle of the two, and right in the middle of 12 and 6 is 9. I hope that made sense, it's tough to explain, sorry! After class someone asked about that problem and my teacher said the correct answer was 8 hours because it was an inverse variation. 10 x 12 = 120 and 20 x 6 = 120. So 120/15=8. I see how she got that, but the problem never said "the amount of workers varies inversely with the amount of time." I was wondering who was right, because I still believe what I did was correct.

Thanks! :)

You must have allowed for tea breaks. Certainly the builders working over here would have taken 6 months to get the scaffolding up let alone build the darn house.
Oh, teacher is correct.

Anna: For these kinds of problems I find it easiest to convert the data to its simplest form. In this case, if it takes 10 workers 12 hours, then that means it takes a total of 120 man-hours. Do you see that? You can check this using the second fact that you were told - if you put 20 workers on the job, then they would complete the house in 120 man-hours/20 men = 6 hours, which agrees with the second piece of data you were given. So how long for 15 workers? 120/15 = 8 hours.

These kind of problems can seem confusing, because it's hard to remember whether to take inverses (like your teacher said to do). I find it easiest to just break it down to the simplest fact, such as in this case determining that it takes 120 man-hours to complete the job, and then use that to figure the rest. Hope this helps!

Nicely explained.10/10