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 July 4th, 2018, 12:06 AM #1 Senior Member   Joined: Aug 2014 From: India Posts: 458 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: 954 Thanks: 342 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: 20,929 Thanks: 2205 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
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Quote:
 Originally Posted by Ganesh Ujwal 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.
Try something solving something funnier like the the following two questions; believe it or not, it will straighten you up.

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
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Quote:
 Originally Posted by skipjack Let c be the fraction of a field that a cow grazes in a day. You can now write two equations: 15(100c - g) = 1 and 30(60c - g) = 1.
How did you write this two equations?

why 1 after "equal to" sign ? why not 2,3, 50,100?

 July 4th, 2018, 03:19 AM #6 Global Moderator   Joined: Dec 2006 Posts: 20,929 Thanks: 2205 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
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Quote:
 Originally Posted by skipjack The "1" is because 1 field is grazed in the 15 days (or 30 days for the second equation).
Why we need to consider grass growing during the grazing time?

July 4th, 2018, 04:48 AM   #8
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Quote:
 Originally Posted by Ganesh Ujwal Why we need to consider grass growing during the grazing time?
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: 14,597 Thanks: 1038 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: 20,929 Thanks: 2205 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! Thanks from jonah, topsquark, weirddave and 1 others

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