SOLUTION: 6 wolves can eat 6 sheeps in 6 days. how many wolves does it take to eat 60 sheep in 60 days? How many days does it take 3 wolves to eat three sheep? Can someone help with this qu

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Question 1162201: 6 wolves can eat 6 sheeps in 6 days. how many wolves does it take to eat 60 sheep in 60 days? How many days does it take 3 wolves to eat three sheep?
Can someone help with this question.
Thanks in advance
Found 3 solutions by ikleyn, josgarithmetic, greenestamps:
Answer by ikleyn(52800) About Me  (Show Source):
You can put this solution on YOUR website!
.

Let x be the number of wolves under the question.


The rate of eating, in the first scenario, is  6_sheeps%2F%286_Wolves%2A6_days%29 = 1%2F6  of the sheep per single wolf per day.


The rate of eating, in the second scenario, is  60_sheeps%2F%28x_wolves%2A60_days%29 = 1%2Fx of the sheep per single wolf per day.


We assume that the rate is the same in both cases, which gives us an equation


    1%2Fx = 1%2F6.


From this equation, you get the 


ANSWER.  6 wolves.

Solved.

You may solve the second problem by the same way  ON  YOUR  OWN  to check if you do understand the idea.

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See the lesson
    - Rate of work problems
in this site.

Find there many other similar problems solved by the same method.

Read this lesson to get the feeling of solid ground under your legs.

These problems will also make your horizon wider.



Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
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6 wolves can eat 6 sheeps in 6 days.
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RATE%2ATIME=WORK

r, the consumption rate for 1 wolf
1 whole piece of work is, "eat one sheep".

%286r%29%2A6=6
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for just one wolf, highlight_green%28r=1%2F6%29----------one sheep in six days
.
.
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Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


There are a wide variety of very different methods for solving problems like this; different methods will work better for different people.

I will show you the method that works best for me.

Start with the given numbers and change two numbers at a time, using common sense, until you have the desired numbers.

6 wolves, 6 days, 6 sheep [given]

60 wolves, 6 days, 60 sheep [it will take 10 times as many wolves to eat 10 times as many sheep in the same 6 days]

6 wolves, 60 days, 60 sheep [it will take 1/10 as many wolves to eat the same 60 sheep if there are 10 times as many days]

ANSWER: It takes 6 wolves to eat 60 sheep in 60 days.

Of course, you can make the jump directly from the given information by changing all three numbers at the same time using logical reasoning:

6 wolves, 6 days, 6 sheep [given]

6 wolves, 60 days, 60 sheep [10 times as many sheep to eat, and 10 times as many days, means the same 6 wolves]

Second problem....

6 wolves, 6 days, 6 sheep [given]

half as many wolves, same number of sheep --> twice as many days:
3 wolves, 12 days, 6 sheep

half as many sheep, same number of wolves --> half as many days:
3 wolves, 6 days, 3 sheep

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Many students find it easy to show the work for this method of solving the problem with a table.

First problem....
   wolves  sheep  days
  ---------------------
      6      6      6
      60     60     6   10 times as many sheep, same number of days --> 10 times as many wolves
      6      60    60   10 times as many days, same number of sheep --> 1/10 as many wolves