My Math Forum  

Go Back   My Math Forum > High School Math Forum > Elementary Math

Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion


Thanks Tree8Thanks
Reply
 
LinkBack Thread Tools Display Modes
July 4th, 2018, 01:06 AM   #1
Senior Member
 
Joined: Aug 2014
From: India

Posts: 342
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.
Ganesh Ujwal is offline  
 
July 4th, 2018, 02:53 AM   #2
Senior Member
 
Joined: Apr 2014
From: UK

Posts: 891
Thanks: 328

You have to take account of the grass growing during the grazing time.
weirddave is offline  
July 4th, 2018, 02:55 AM   #3
Global Moderator
 
Joined: Dec 2006

Posts: 19,865
Thanks: 1833

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.
skipjack is offline  
July 4th, 2018, 02:58 AM   #4
Senior Member
 
Joined: May 2008

Posts: 297
Thanks: 81

Beer soaked counter questions follow.
Quote:
Originally Posted by Ganesh Ujwal View Post
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 days—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?
jonah is offline  
July 4th, 2018, 03:38 AM   #5
Senior Member
 
Joined: Aug 2014
From: India

Posts: 342
Thanks: 1

Quote:
Originally Posted by skipjack View Post
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?
Ganesh Ujwal is offline  
July 4th, 2018, 04:19 AM   #6
Global Moderator
 
Joined: Dec 2006

Posts: 19,865
Thanks: 1833

The "1" is because 1 field is grazed in the 15 days (or 30 days for the second equation).
skipjack is offline  
July 4th, 2018, 04:40 AM   #7
Senior Member
 
Joined: Aug 2014
From: India

Posts: 342
Thanks: 1

Quote:
Originally Posted by skipjack View Post
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?
Ganesh Ujwal is offline  
July 4th, 2018, 05:48 AM   #8
Senior Member
 
Joined: Apr 2014
From: Glasgow

Posts: 2,132
Thanks: 717

Math Focus: Physics, mathematical modelling, numerical and computational solutions
Quote:
Originally Posted by Ganesh Ujwal View Post
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?
Benit13 is offline  
July 4th, 2018, 06:09 AM   #9
Math Team
 
Joined: Oct 2011
From: Ottawa Ontario, Canada

Posts: 13,444
Thanks: 946

As an aside: if grass grows constantly, field will never be "completely" grazed!
Denis is offline  
July 4th, 2018, 09:17 AM   #10
Global Moderator
 
Joined: Dec 2006

Posts: 19,865
Thanks: 1833

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
skipjack is offline  
Reply

  My Math Forum > High School Math Forum > Elementary Math

Tags
confusing, question, solve



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
please help me with this confusing question?? kozhin Calculus 1 February 17th, 2013 02:56 PM
Confusing probability question HungerGames1 Probability and Statistics 3 April 2nd, 2012 07:40 AM
Probability (confusing question) hoyy1kolko Probability and Statistics 5 April 15th, 2011 11:22 PM
Matrix question (confusing) hoyy1kolko Algebra 5 December 30th, 2010 09:28 PM
Confusing Question xnarutox Algebra 5 September 11th, 2010 04:22 PM





Copyright © 2018 My Math Forum. All rights reserved.