Solving Car Overtaking Length with 50mi/h and 45mi/h Cars

[rigor]

A car going 50mi/h overtakes and passes another car moving at 45mi/h. What length of road is required for the operation? Assume that each car is 15ft. long and that there is a 60ft. space between them before and after passing. Taking into account the approach of a car from the opposite direction at 50mi/h, what clear length of road is required?

The anwer here is 1500ft and 3000ft. How was that?? Please show to me the solution.. Thanks...

 

[Vanadium 50]

Hi Rigor,

What did you try? How far did you get?

PS It is helpful to describe the problem in the subject line. Variations on "I need help" are not helpful when trying to locate a particular thread.

 

[HallsofIvy]

The simplest way to do this is to look at it from the slower car's reference system. That is, treat the slower car as if it were standing still and the faster car moving at 50- 45= 5 miles per hour. The faster car starts 60 feet behind and winds up 60 feet ahead so it must go 120 feet. How long does it take to go 120 feet at 5 miles per hour? You will need to convert from miles per hour to feet per minute or feet per second.

Now put that 45 m/h back in. In the time you just found, how far will the slower car have gone? The faster car must go 120 feet faster than that. Or you could just multiply that time by 50 mph to find the distance required by the faster car.

And how far will the car approaching car go in that time? You will need to add that to the distance you just found to find a distance to assure that the cars do not run into each other.