At what time will runner B catch up with runner A?

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In summary, Runner A, who runs with an average speed of 3.0 m/s, starts out at 3:00 P.M. Runner B, who runs with an average speed of 4.0 m/s, starts after A from the same place exactly 5 min later. At what time will runner B catch up with runner A? If the runners stop when B catches A, how far do they run? If I let the time A runs be "t", then the time B runs is "t- 5". So... 4.0 m/s= 3.0-5 and 3.0= t. If I'm on the right track, then B's equation would be t=2.1
  • #1
JohnQ
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Runner A, who runs with an average speed of 3.0 m/s, starts out at 3:00 P.M. Runner B, who runs with an average speed of 4.0 m/s, starts after A from the same place exactly 5 min later.
a.) At what time will runner B catch up with runner A?
b.) If the runners stop when B catches A, how far do they run?

So far I have 4.0 m/s*300 s = 1.2 Km and 3.0 m/s x 300s= 0.9 km, but I don't even know if this is the right aproach, can anyone help me from here?
 
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  • #2
They are two linear equations(with one solution I believe), find the point of intersection.

I will not tell you the answer, but merely try to open your eyes.

You know the velocities of A and B.

What formula do you use to find the velocity?

Try to combine the formulas to come up with an answer.

Hint: You need to use algebra. The distance traveled must be equal for both because that is when B catches up to A.

Show me some more work, and I'll be back to give more advice.

Note: I can tell you more right now, like most people, but doing it on your feels so much better.
 
  • #3
Trying

so...
If I let the time A runs be "t", then the time B runs is "t- 5".
...4.0 m/s= t-5
and 3.0= t

So... 4.0 m/s= 3.0-5
I'm I on the right track?
 
  • #4
Huh?

To take that route I believe you will need to convert the minutes into seconds since your velocity is 4.0m/s.

Look at what you wrote. You said 4=3-5. We know that's incorrect already.

The formula for velocity is [tex]v=d/t[/tex].

Because there is two different velocities, there is two different equations to work with.

With the two equations that you get, combine them.

Note: Remember, d will be the same for both.
 
  • #5
Still trying

so...for B v=1.2 km/ 3.0

and for A v= .9 km/3.0, IF RIGHT, WHAT UNITS IS 3.0 IN, HR?
 
  • #6
Wrong. I'm having a hard time trying to understand where you got this.

I'll give you the equation for B, since you kind of got it in your second post. A is very similiar.

[tex]4.0m/s = \frac{d}{t_1-300s}[/tex] , 300s = 5min (converted into seconds).

You had t-5, but that was incorrect. Find equation A. Remember d is the same for both.

Combine both equations by isolating a term(d or t_1).

Note: I must go bang my head trying to fully comprehend SR.

Hopefully someone takes over if you are still stuck.
 
  • #7
Also, read the first 2 chapters of your textbook. It will talk about dimensionalities(metres, seconds) and most likely average velocities.

That would help a lot.

There is also a forum for homework help, and they have helpful people there. Believe it or not, they have regulars for helping out.

Please avoid homework related problems in this forum. I made the mistake myself, so it's not big deal, so I'm letting you know.
 
  • #8
?

so distance equal to 2.1?
 
  • #9
Let's start with runner a.

If runner a moves at a velocity of 3 m/s, and he runs for 1 second, how many meters does he move?

If he runs for 2 seconds, how many meters does he move?

More advanced:
Can you write an equation for the position of runner a as a function of time?
 
  • #10
That's what I was saying. I even gave the equation itself.

I would love to show you how it's done, but it is better to work it out yourself. Once you get that breakthrough, everything else becomes a little easier.

Note: The answer might be 2.1m because I never checked.
 

Related to At what time will runner B catch up with runner A?

1. How do you calculate the time when runner B will catch up with runner A?

To calculate the time, you need to know the distance between the runners, the speed of runner A, and the speed of runner B. Then, you can use the formula t = d / (vB - vA) where t is the time, d is the distance, and vA and vB are the speeds of runner A and B respectively.

2. What if runner B is running faster than runner A, will they ever catch up?

Yes, if runner B is running faster than runner A, they will eventually catch up. This is because the distance between them will decrease with time, and eventually become zero at the point of intersection.

3. Can this formula be used for any type of race?

Yes, this formula can be used for any type of race where one runner starts at a certain distance ahead of the other and they are both running at constant speeds.

4. Is there a simpler way to calculate the time when runner B will catch up with runner A?

Yes, you can also calculate the time by dividing the distance between the runners by the difference in their speeds. This formula is t = d / (vB - vA).

5. Can this formula be used for multiple runners?

No, this formula can only be used for two runners. If there are more than two runners, a different formula or approach would be needed to calculate when one runner will catch up with another.

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