SOLUTION: A lion eats one sheep in 4 hours, a leopard eats one sheep in 5 hours, and a bear eats one sheep in 6 hours. How long would it take the three animals together to eat one sheep? HIN

Algebra ->  Algebra  -> Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A lion eats one sheep in 4 hours, a leopard eats one sheep in 5 hours, and a bear eats one sheep in 6 hours. How long would it take the three animals together to eat one sheep? HIN      Log On

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Question 184332: A lion eats one sheep in 4 hours, a leopard eats one sheep in 5 hours, and a bear eats one sheep in 6 hours. How long would it take the three animals together to eat one sheep? HINT: How much of one sheep do they eat together in one hour?
Answer by Alan3354(21612) About Me  (Show Source):
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A lion eats one sheep in 4 hours, a leopard eats one sheep in 5 hours, and a bear eats one sheep in 6 hours. How long would it take the three animals together to eat one sheep? HINT: How much of one sheep do they eat together in one hour?
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This type of problem is tricky at first. You have to use the inverses, sheep per hour, instead of hours per sheep. Then you have the same units and you can add them.
You have 1/4 sheep/hr
1/5 and 1/6
Add them: 1/4 + 1/5 + 1/6 = 15/60 + 12/60 + 10/60
= 37/60 sheep/hour
Invert that to get 60/37 hours/sheep
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A shortcut is product/permutations of sums, 2 at a time)
=4*5*6/(4*5+4*6+5*6)
= 120/(20+24+30) = 120/74
=60/37 (same answer)