July 4th, 2018, 12:06 AM  #1 
Senior Member Joined: Aug 2014 From: India Posts: 343 Thanks: 1  How to solve this confusing question?
100 cows can graze a field completely in 15 days, while 60 cows can do it in 30 days. How many cows are needed to do it in 10 days? Answer is 140 cows I tried: It'd seem like it'd only take 50 cows to graze a field in 30 days if 100 can do it in 15. But in question it shows 60 cows can do it in 30 days. I am confused with this question. 
July 4th, 2018, 01:53 AM  #2 
Senior Member Joined: Apr 2014 From: UK Posts: 903 Thanks: 331 
You have to take account of the grass growing during the grazing time.

July 4th, 2018, 01:55 AM  #3 
Global Moderator Joined: Dec 2006 Posts: 20,464 Thanks: 2038 
Let c be the fraction of a field that a cow grazes in a day. Let g be the fraction of a field that grows in a day, and assume that g is a constant. You can now write two equations: 15(100c  g) = 1 and 30(60c  g) = 1. Solving those gives c = 1/1200 and g = 1/60. If n cows can graze the field completely in 10 days, 10(n/1200  1/60) = 1, so n = 120(1 + 1/6) = 140. 
July 4th, 2018, 01:58 AM  #4  
Senior Member Joined: May 2008 Posts: 299 Thanks: 81  Beer soaked counter questions follow. Quote:
A man can drink a cask of wine in 20 days, but if his wife drinks with him it will take only 14 daysâ€”how long would it take for the wife alone? If one priest can pray a soul out of purgatory in 5 hours, while it takes a second priest 8 hours, how long will it take if the two priests prayed together?  
July 4th, 2018, 02:38 AM  #5 
Senior Member Joined: Aug 2014 From: India Posts: 343 Thanks: 1  
July 4th, 2018, 03:19 AM  #6 
Global Moderator Joined: Dec 2006 Posts: 20,464 Thanks: 2038 
The "1" is because 1 field is grazed in the 15 days (or 30 days for the second equation).

July 4th, 2018, 03:40 AM  #7 
Senior Member Joined: Aug 2014 From: India Posts: 343 Thanks: 1  
July 4th, 2018, 04:48 AM  #8 
Senior Member Joined: Apr 2014 From: Glasgow Posts: 2,150 Thanks: 730 Math Focus: Physics, mathematical modelling, numerical and computational solutions  Well, like you said in your first post, you were expecting that 50 cows would be needed to graze the field in 30 days, but that's not the case. Instead, it is 60. What reasons could there be for needing more cows to graze the field?

July 4th, 2018, 05:09 AM  #9 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,276 Thanks: 1023 
As an aside: if grass grows constantly, field will never be "completely" grazed!

July 4th, 2018, 08:17 AM  #10 
Global Moderator Joined: Dec 2006 Posts: 20,464 Thanks: 2038 
Every cow was Kung Fu grazing, Those cattle were faster than lightning! In fact, it was a little bit frightening... But they mowed with expert timing! 

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