If street lights are placed at most 132 feet apart, how many street lights will be needed for a street that is 4 miles long, assuming that there are lights at each side of the street?

1 Answer
May 13, 2016

If lights need to be placed across from each other down the street,
then at least 322322 lights will be needed.

Explanation:

interpretation 1
"lights at each side of the street" means that lights are to be placed across from each other down the street.

In this case the number of lights needed will be twice the number of lights needed along one side of the street with a maximum of 132 feet between these lights.

4 " miles" =4xx5280 " feet"4 miles=4×5280 feet
and with 132" feet"132 feet per interval between poles
we would need
color(white)("XXX")(4xx 5280" feet")/(132" feet")XXX4×5280 feet132 feet

color(white)("XXX")=160XXX=160 intervals between poles

Since we need to start with a pole (at distance 00) and need 160160 more poles
we will need 161161 poles on each side of the street

or a total of 161xx2=322161×2=322 poles for both sides of the street.

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interpretation 2
If we can alternate the poles on opposite sides of the street we can (probably) accomplish this with fewer poles.
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Without knowing the distance across the street we can not be sure of how many posts would be required.

For demonstration purposes if the color(blue)("distance across the street")distance across the street was approximately 3333 feet so that the component of the displacement between street lights in the direction of the street was color(green)(128" feet")128 feet

Then there would be
color(white)("XXX")(5280xx4)/128 = 165XXX5280×4128=165 intervals
and
color(white)("XXX")166XXX166 poles would be needed.