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(39618) (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(52797) (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.