Two cars are driving toward each other from opposite directions. If one is driving 55 mph, the other is driving 60 mph and the cars are 500 miles apart, how long will it be before they pass each other? Round to the nearest tenth of an hour.
A. 4.3 hours
B. 4.5 hours
C. 5.1 hours
D. 4.8 hours

Question

Two cars are driving toward each other from opposite directions. If one is driving 55 mph, the other is driving 60 mph and the cars are 500 miles apart, how long will it be before they pass each other? Round to the nearest tenth of an hour.
A.	4.3 hours
	B.	4.5 hours
	C.	5.1 hours
	D.	4.8 hours

alfie · Answer

Hint: I'd work first on the position, in order for them to "pass each other" they must be in the same position.
So.

$$x_{f.car1} = x_{f.car2}$$

anonymous · Answer

ok thanks

alfie · Answer

You are welcome. Some other stuff:

if you assume the first car to be driving in the positive direction, the second car will go in the negative direction.
The first car initial position is going to be 0miles.
The second car initial position is going to be 500miles.

$$x_{f1} = v_i t$$ where vi is specified in the problem.

$$x_{f2} = x_i + v_i t$$

Where xi = initial position of second car, and vi is the velocity of the second car (remember, it is driving in the negative direction!)

Good luck, tell me what's your result when you are done :)

anonymous · Answer

ok i will tell you when i am done! :)

anonymous · Answer

you can simply work it out from the reference frame of one of the vehicles and therefore give the other the velocity of both cars added together. so car one has v=0 car two has v=115 mph then just use speed=distance/time to find that t=500/115=4.348 hours so ans is a 4.3 hours. you can us this method when the objects are at constant speed or if they are accelerating you would have to add the average speeds of the cars over the time they travel for.  hope this helps