A man drove at a steady speed along a highway passing a certain advertising sign that was regularly spaced along the road. He counted the number of signs he passed in one minute, and noticed that \(10\) times that number equaled the speed of the car in miles per hour. How far is it between one sign and the next?

A man drove at a steady speed along a highway passing a certain advertising sign that was regularly spaced along the road. He counted the number of signs he passed in one minute, and noticed that \(10\) times that number equaled the speed of the car in miles per hour. How far is it between one sign and the next?

Let \(N=\) the number of signs passed in one minute.

Then \(60N\) will be the number of signs passed in one hour.

The speed of the car is given to be \(10\) times the number of signs passed in one minute, or \(10N\text{ miles per hour}\). Therefore in \(10N\text{ miles}\) it will pass \(60N\text{ signs}\).

If the car passes \(60N \text{ signs}\) in \(10N\text{ miles}\), it must pass \(60N/10N\) or \(6\text{ signs}\) in one mile.

So if the car passes \(6\text{ signs}\) in one mile (\(5280\text{ feet}\)), the distance between signs must be \(5280/6\) or \(880\text{ feet}\).

It is surprising that this problem can be solved without knowing the actual speed of the car.

(Solutions to this type of problem lend themselves to a branch of mathematics called Dimensional Analysis, but I think you are probably at least a year or so away from being able to apply this approach.)