# Car speed and distance problem

• aricho

#### aricho

Bart simpson drove at a steady speed along the pacific highway with his mother beside him

"have you noticed," he said "that the McDonalds signs seem to be evenly spaced along the side of the road? i wonder how far apart they are"

Mrs Simpson glanced at her watch, then counted the number of mcdonalds signs they passed in one minute.

What a strange coincidence" exclaimed bart, "when you multiply the number by 10 it is exactly equal to the speed of our car in km/h (kilometers per hour)

Assuming that the car is traveling at a constant speed and the minute began and ended midway between the 2 signs, how far is it between one sign and the next?

I have the answer, it's 166.67 meters, found by:

Suppose they pass 6 signs, so the speed is 60km/h
therefore 1km/minute
1km/6signs=0.16(repepater) km

try with 8, 10,200, all equals the same in the end.

So, my question is, how do i write this algebraically, what is the formal method?

Let x be the distance between two signs, in km. If you pass n signs, the you have traveled nx km (there are n-1 intervals between the signs and you start and end the minute half way between signs which adds another x interval). Therefore, if you pass n signs in one minute, your speed is nx km per minute or 60nx km/hr. We are told that the number of signs times 10 is equal to the speed in km/hr: 10n= 60nx. Very conveniently, the n's cancel and x= 10/60 = 1/6 km just as you got. Frankly, I prefer your method!

HallsofIvy said:
Let x be the distance between two signs, in km. If you pass n signs, the you have traveled nx km (there are n-1 intervals between the signs and you start and end the minute half way between signs which adds another x interval). Therefore, if you pass n signs in one minute, your speed is nx km per minute or 60nx km/hr. We are told that the number of signs times 10 is equal to the speed in km/hr: 10n= 60nx. Very conveniently, the n's cancel and x= 10/60 = 1/6 km just as you got. Frankly, I prefer your method!

Sorry to bother you, but why are there n-1 intervals between each sign?

If there is 1 sign, there are no intervals.
If there are 2 signs, there is one interval bwteween the first sign and second sign.
If there are 3 signs, there are 2 intervals, the first interval between the first and second signs, the second inetrval between the second and third sign.

So if there are n signs, there are n-1 intervals between the signs.