Calculating Time and Distance: Solving for When Two Objects Will Meet

[drcathyc]

Two men start out at time 0. Man A is traveling at 3.2 kph. Man B is traveling at 6 kph. Man A starts out 35 k ahead of man B. How long will it take for B to catch A?

I know this is a simple question for many of you, but I just can't recall how to solve it. Please help.

 

[arildno]

1. Let the (spatial) origin be placed at B's original position

2. State A's position, as measured from the origin, as a function of time.
3. Do the same with B's position.
4. Formulate the equation for time t when A and B are at the same position

 

[drcathyc]

1. Let the (spatial) origin be placed at B's original position

2. State A's position, as measured from the origin, as a function of time.
3. Do the same with B's position.
4. Formulate the equation for time t when A and B are at the same position

Ok, A's position at time 0 is 5.8 hours ahead of B if B travels at 6 kph. I don't know the spatial point when B overtakes A and I don't know the time. I'm still confused.

 

[arildno]

A's position from the spatial origin at time t=0 is 35 kilometers, agreed?

So, assume that time "t" has passed, how far is A from the origin?

 

[drcathyc]

A's position from the spatial origin at time t=0 is 35 kilometers, agreed?

So, assume that time "t" has passed, how far is A from the origin?

35k + t(3.2kph) ?

 

[arildno]

Correct!

And, after time "t", how far away from the origin has B come?

 

[drcathyc]

0 + t(6.0kph) ?

 

[arildno]

Quite so!

Now, what equation must hold when A and B are at the SAME position at the SAME time "t"?

 

[drcathyc]

35 + t(3.2) = 0 + t(6.0) ??

 

[arildno]

Again, correct!

Now, solve that equation for "t"

 

[drcathyc]

6t - 3.2t = 35
2.8t = 35
t = 35/2.8
t = 12.5 !

 

[arildno]

and you're done..

 

[drcathyc]

Thank you so much for your help. As a psychologist, I've probably forgotten more math than I ever learned (except maybe statistics). I'm working on an Science Fiction novel and needed to plot out this situation. Again, thanks, particularly for walking me through in developing the equation rather than simply supplying the answer. Your help is well appreciated.

 

[arildno]

You're welcome, I hope you enjoyed the trip.
I did.

 

[drcathyc]

I did enjoy the trip.And realized that my plot line wouldn't work with that solution. The good guys (A) would get wiped out by the bad guys (B). Without the help, I would have written an entirely unrealistic scene.

 

[arildno]

I think it is great that you devote enough attention to "the little details" like maths. I've read my share of novels where the author's lacking grasp on numbers (as in, for example, logistics or the necessary time interval to complete something) Mars an otherwise good story.

Good luck with your writing!