Hello, Mr_Green!
Everyone seems to have overlooked the essential piece of data:
. . the lengths of the cars.
A 35-mph car is driving down the street.
It catches up to a slow poke car going 15 mph.
The 35-mph car wants to pass him.
How much room (distance) will he need to pass the 15-mph car? If the cars are considered to be POINTS,
. . it takes only an instant to complete the passing.
Assuming the cars have length feet,
. . the faster car overtakes the slower car
. . when F's front bumper is even with S's rear bumper.
And that is when we begin measuring time and distance. Code:
L
*---------*
| S | →
*---------*
L
*---------*
| F | →
*---------*
At some point down the road, F has passed S.
F's rear bumper is even with S's front bumper.
And F has travelled a distance Code:
L
*---------*
| S | →
*---------*
L
*---------*
| F | →
+ - - - - - - d - - - - - - *---------*
Relative to , must travel a distance of feet.
Relative to , 's speed is: .
This will take: . seconds.
At travels: .
Therefore, it takes 3½ car lengths.