# Word Problem-Calculus

• May 31st 2010, 10:40 AM
skweres1
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?

• May 31st 2010, 10:50 AM
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.
• May 31st 2010, 12:10 PM
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?
• May 31st 2010, 02:18 PM
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: $\displaystyle Time = 1500 / (50/6 + 50/9) = 30/(1/6 + 1/9) = 108 min$
• Jun 1st 2010, 06:25 AM
Unknown008
Quote:

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. (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.
• Jun 1st 2010, 12:15 PM
HallsofIvy
Quote:

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?