How to Solve for Distance and Time in a Two-System Motion Problem

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To solve the problem of when the hounds catch the mechanical rabbit, set up equations for the positions of both the hounds and the rabbit using the formula X = Xi + Vt. The hounds are running at 23.0 m/s and start 66.0 m behind, while the rabbit moves at 6.0 m/s. By equating the two position equations, you can solve for the time it takes for the hounds to catch up and the distance the rabbit travels during that time. Since both are moving at constant speeds, acceleration is not a factor in this scenario. This approach allows for determining both the time until the rabbit is overtaken and the distance it covers before that happens.
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Homework Statement



a pack of hounds running at 23.0m/s is 66.0m behind a mechanical rabbit, itself sailing along at 6.0m/s.

Homework Equations

a) how long will it take before the rabbit is caught? b) how far will it travel before being over taken?



The Attempt at a Solution


I can't even figure out where to start. I tried Vit + 1/2 At2-x . I just can't figure how to set this up.
 
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Both hounds and rabbit are moving at constant speed so there's no acceleration to worry about. The key formula is X = Xi + Vt.

Write expressions (using the formula above) for the position of hounds and rabbit, then solve them together to find the time.
 
OK. So you have two different systems here, the pack of dogs and the rabbit. They are both moving at different rates and you want to know when they are at the same place.

Can you give me an equation that describes the motion of the rabbit? the pack? If you can you would have two equations both in terms of position and time. Then you have two equations and two unknowns, you should be able to solve for both.

EDIT: You beat me to it Doc Al!
 

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