Three cows

Algebra Level 2

A farmer has three cows, A, B and C

Cow A has a good appetite and always finishes the grass provided in 20 minutes.

Cow B eats in a moderate speed and always finishes the grass provided in 30 minutes.

Cow C is extremely lazy and always finishes the grass provided in an hour.

Given such information, if they all eat together, how much time do they need? Give your answer in minutes.

Details and Assumptions:

The farmer provides the same amount of grass every time.

The answer is 10.

3 solutions

Fox To-ong
Feb 23, 2015

that's 1/t = 1/20 + 1/30 + 1/60 t = 10

Eshan Uniyal
Sep 27, 2014

Cow A eats grass x in 20 minutes, therefore in 1 minute it eats x/20 of the grass and so on, with Cow B eating x/30 of the grass and Cow C eating x/60 of the grass. Adding their consumption in 1 minute, we get x/20+x/30+x/60=6x/60=x/10 Therefore, the cows together eat x/10 of grass x in one minute. Therefore, the cows will take 10 minutes to finish all of the glass.

Carl Patel
Sep 12, 2014

Cow A eats 1/20th of the grass in a minute Cow B eats 1/30th of the grass in a minute Cow C eats 1/60th of the grass in a minute Taking the summation of the above numbers, we have the total grass eaten by all three in a minute, which comes to - 6/60 Hence it takes 6 minutes for all three to finish the grass.

They eat at a rate of 6/60, so it will take them 60/6 = 10 minutes to eat it all.

I have updated the answer accordingly.

Calvin Lin Staff - 6 years, 9 months ago

Three cows

The answer is 10.

3 solutions

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