# Word Problem-Calculus

#### skweres1

It takes one corn mill 6 minutes to grind a 50 pound bag of corn into cornmeal, while it takes a slower mill 9 minutes to grind the same bag of corn. If both mills are working at the same time, how long would it take to grind 1500 pounds of corn?

#### Unknown008

If they work together, they should take less time to make a 50 pound bag.

This time is given by:

$$\displaystyle \frac{1}{t_1} + \frac{1}{t_2} = \frac{1}{t_{total}}$$

Using the given values, we get:

$$\displaystyle \frac{1}{6} + \frac{1}{9} = \frac{5}{18}$$

So, the total time is 18/5 = 3.6 hours.

It takes 3.6 hours to make a 50 pound bag.

You can now use proportions to find the time it takes for 1500 pound of corn to be gound.

#### skweres1

Thanks

Thank you, but if it takes 6 minutes for one person to do 50 pounds then how would it take 3.6 hours to to it together?

• Unknown008

#### GeoC

Rate Mill 1: $$\displaystyle R_1 = 50/6$$
Rate Mill 2: $$\displaystyle R_2 = 50/9$$

Combined Rate $$\displaystyle R_t = R_1 + R_2$$

Thus: $$\displaystyle Time = 1500 / (50/6 + 50/9) = 30/(1/6 + 1/9) = 108 min$$

#### Unknown008

Thank you, but if it takes 6 minutes for one person to do 50 pounds then how would it take 3.6 hours to to it together?
Right, actually, I it was 3.6 minutes, and not 3.6 hours. (Itwasntme)

Then, taking from there, you can use proportions to solve the rest.

50 pounds are ground in 3.6 minutes.
1 pound is ground in 3.6/50 minutes.
1500 pounds are ground in 3.6/50 * 1500 = 108 minutes.

#### HallsofIvy

MHF Helper
It takes one corn mill 6 minutes to grind a 50 pound bag of corn into cornmeal, while it takes a slower mill 9 minutes to grind the same bag of corn. If both mills are working at the same time, how long would it take to grind 1500 pounds of corn?