Word Problem-Calculus

Dec 2009
30
1
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?



Please Help, Thanks!!!!
 
May 2010
1,260
410
Mauritius
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.
 
Dec 2009
30
1
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?
 
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May 2010
43
1
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: \(\displaystyle Time = 1500 / (50/6 + 50/9) = 30/(1/6 + 1/9) = 108 min\)
 
May 2010
1,260
410
Mauritius
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
Apr 2005
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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?



Please Help, Thanks!!!!
When two or more things work together, their speeds ad. The speed of the fist corn mill is 50 pounds per 6 minutes or 50/6= 25/3 pounds per minute. The speed of the second is 50/9 pounds per minute. Together they can grind 50/9+ 25/3= 50/9+ 75/9= 125/9 pounds per minute. The will grind 1500 pounds in (1500)(125/9) minutes.