SOLUTION: The force F required to open a gate varies inversely as the distance d of the force from the line of hinges. The least force that can be used to open a certain gate 8 feet wide is

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Question 1094674: The force F required to open a gate varies inversely as the distance d of the force from the line of hinges. The least force that can be used to open a certain gate 8 feet wide is 10 lbs. What force applied at a distance of 15 inches from the hinges would be needed to open the gate?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
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force F required to open a gate varies inversely as the distance d of the force from the line of hinges.
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for a constant, k.

and from this,
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
The ratio of the forces is    dimensionless units.


The ratio of the distances (measured in inches) is    in the same order.    (Notice 8 feet = 8*12 inches !)


In accordance with the condition, you should equate/write inverse proportion


 = .


Then F =  = 64 lbs.


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