What is the time difference between two cars when traveling at different speeds?

[hemang]

Two cars, A and B, are traveling in the same direction, although car A is 208 m behind car B. The speed of A is 25.7 m/s, and the speed of B is 18.6 m/s. How much time does it take for A to catch B?
Time it takes for A to catch B is
speed=distance/time
time=distance/speed
=208/25.7
=8.09s

Is that right.
if not, help me
thanks

 

[cristo]

No, you're not correct. If you want to use that formula, you need to consider the difference between the speeds of the two cars, not the speed of car A.

 

[hemang]

I don't get it. could u describe clearly?

 

[hemang]

car A: time=(d-208)/25.7
so, d=(25.7m/s)t + 208m
car B: time=(d+208)/18.6
so, d=(18.6m/s)t-208

(25.7m/s)t + 208m = (18.6m/s)t - 208m
(7.10m/s)t = -416m
t= (-416m)/(7.10m/s)
t=58.6 seconds
Is this right?

 

[cristo]

No, this is not correct, but you're getting closer! Look at the distances you have assigned to the cars. According to your equations, how far behind B is car A at t=0?

We want to find the time when the displacements of the two cars are equal. Let's say that at a distance d from car B's initial position, car A catches it up. How far does car A have to travel to reach this point? This should help you set up your equations.

 

[hemang]

so, would that be 208-d?

 

[hemang]

t for A: (208m-d)/25.7m/s
so, d= 208m-(25.7m/s)t
t for B: (208+d)/18.6m/s
so, d= (18.6m/s)t-208m

(18.6m/s)t-208m = 208m- (25.7m/s)t
t=416m/44.3m/s
=9.39 seconds
what about this?

 

[hemang]

help please- urgent

Two cars, A and B, are traveling in the same direction, although car A is 208 m behind car B. The speed of A is 25.7 m/s, and the speed of B is 18.6 m/s. How much time does it take for A to catch B?

help me with equations.

 

[cristo]

Two cars, A and B, are traveling in the same direction, although car A is 208 m behind car B. The speed of A is 25.7 m/s, and the speed of B is 18.6 m/s. How much time does it take for A to catch B?

help me with equations.

There's no need to repost the question.

so, would that be 208-d?

No, car A need to travel more distance.. so the total distance will be 208+d.

t for A: (208m-d)/25.7m/s
so, d= 208m-(25.7m/s)t
t for B: (208+d)/18.6m/s
so, d= (18.6m/s)t-208m

(18.6m/s)t-208m = 208m- (25.7m/s)t
t=416m/44.3m/s
=9.39 seconds
what about this?

You didn't listen to what I said. Again, when t=0, the distance between the two cars in your equations is 416m.. this is not correct.

Let the distance B covers be equal to d. Then, car A will have to travel 208+d to reach the same point. Try writing equations with these values for distance.

 

[hemang]

thanks. i got it.
(25.7m/s)t=(18.6m/s)t-208
t=208m/(7.10m/s)
t=29.3 seconds