# Math Help - Word Problem-Calculus

1. ## Word Problem-Calculus

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?

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

This time is given by:

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

Using the given values, we get:

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

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.

3. ## 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?

4. Rate Mill 1: $R_1 = 50/6$
Rate Mill 2: $R_2 = 50/9$

Combined Rate $R_t = R_1 + R_2$

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

5. Originally Posted by skweres1
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.

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.

6. Originally Posted by 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?