Homeschool Math Blog

Here's another one of those job / workers word problems (inverse or direct variation). Try and see if you can solve it using the "table" method instead of equations: A certain job can be done by 18 clerks in 26 days.  How many clerks are needed to perform the job in 12 days? Again, we can set up a table and reason this out. Initially set it up like this: jobs | clerks | days -------------------------- 1 | 18 | 26 -------------------------- 1 | | -------------------------- 1 | ? | 12 Then think of the "days" column. We want to "go" from 26 to 12. You could use a proportion here... or first figure out how many clerks are needed to do this job in 2 days, and then from that go to 12 days. If 18 clerks do it in 26 days, then how many clerks would do it in 2 days... which is 1/13 the amount of time.... so we need 13 times as many clerks. 13 x 18 = 234 clerks are needed. jobs | clerks | days -------------------------...

Today I want to feature a great video from a fellow blogger and Youtuber, Dave Marain. He solves this question, which at first can sound intimidating: If 10 workers can build 3 houses in 60 days, how many workers are needed to build 5 houses in 40 days? It sounds like you'd need algebra, proportions, inverse or direct variation, etc. And true, you could use those. But his method completely avoids all that and is based on setting up a simple TABLE, AND using common sense! | HOUSES | WORKERS | DAYS | ---------------------------------- | 3 | 10 | 60 | ---------------------------------- | 1 | 10 | | ---------------------------------- | 2 | 10 | | ---------------------------------- | 5 | | | ---------------------------------- See the video below: And here's a link to his other Youtube videos: www.youtube.com/user/MathNotationsVids .

Dave Marain recently featured my blog on his, and now it just so happens I get to promote his, because I really liked his post about learning direct and inverse variations . He uses a beagle problem with interesting numbers: "Three beagles can dig 4 holes in five days. How many days will it take 6 beagles to dig 8 holes?" The solution is actually quite easy — just think how there are exactly twice as many beagles and also twice as many holes. Dave shows a chart that can help youngsters grasp the solution. I want to go one step further with this. Let's try a little more awkward numbers: "Three beagles can dig 7 holes in eight days. How many days will it take 5 beagles to dig 9 holes?" I want to show you how a "chart" approach will still work. This situation describes joint variation , because there is both inverse and direct variation involved: the number of days it takes to dig the holes varies inversely with the number of beagles (the more beagles, ...