SOLUTION: A lion can eat a sheep in 2 hours, a wolf can eat a sheep in 3 hours, and a dog can eat the sheep in 6 hours. How long would it take a lion, a wolf, and a dog all together to eat t

Question 1163362: A lion can eat a sheep in 2 hours, a wolf can eat a sheep in 3 hours, and a dog can eat the sheep in 6 hours. How long would it take a lion, a wolf, and a dog all together to eat the poor sheep?
Found 3 solutions by jim_thompson5910, ikleyn, greenestamps:
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!

The lion can eat the sheep in 2 hours, so its rate is 1/2 of a sheep per hour. In other words, every hour, the lion eats 1/2 a sheep. The wolf's rate is 1/3 of a sheep per hour while the dog's rate is 1/6 of a sheep per hour.

If they divide the work equally, and don't get in each other's way, then their combined rate is
1/2 + 1/3 + 1/6
3/6 + 2/6 + 1/6
(3+2+1)/6
7/6

Their combined rate is eating 7/6 of a sheep per hour. In one hour, they can get a full sheep, plus 1/6 of one

Let x be the number of hours it takes to do the job if they work together. This multiplies with the combined rate and we set this equal to 1 to indicate a full job has been completed

(combined rate)*(number of hours) = 1 full job done
(7/6)*x = 1
x = (6/7)*1
x = 6/7

It takes 6/7 of an hour to get the job done if they work together.

Answer: 6/7 of an hour

Answer by ikleyn(52788)   (Show Source): You can put this solution on YOUR website!
.

Their individual eating rates are , and of a sheep per hour. Their combined eating rate is of a sheep per hours, which is = = = 1 (one sheep per hour). It means that they will complete eating in one hour. ANSWER

Solved.

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It is a standard and typical joint work problem for 3 participant.

There is a wide variety of similar solved joint-work problems with detailed explanations in this site. See the lessons
    - Using Fractions to solve word problems on joint work
    - Solving more complicated word problems on joint work
    - Selected joint-work word problems from the archive
    - Joint-work problems for 3 participants (*)

Read them and get be trained in solving joint-work problems.

The most closed lesson to your problem marked (*) in the list.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this textbook under the topic
"Rate of work and joint work problems" of the section "Word problems".

Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.

Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

Here is an alternative method for solving "working together" problems that many students like because it avoids working with fractions.

Consider the least common multiple (LCM) of the three given times. The LCM of 2, 3, and 6 is 6.

Consider what the lion, wolf, and dog could eat in those 6 hours:
lion: 6/2 = 3 sheep
wolf: 6/3 = 2 sheep
dog: 6/6 = 1 sheep

In 6 hours, the lion, wolf, and dog together could eat 3+2+1=6 sheep.

That means the number of hours they would take to eat the one sheep is 6/6 = 1.

ANSWER: 1 hour for the three together to eat the sheep.

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