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(52787)  (Show Source):
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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