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Question 664540: Can you help me solve this problem: A rabbit is 30 feet from its burrow. It can run 25 feet per second. A coyote that can run 50 feet per second spots the rabbit and starts running toward it. Write expressions for the time it will take the rabbit to get to its burrow and for the time it will take the coyote to get to the burrow. Then, write and solve an equation that relates to the two expressions.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! rate * time = distance.
r = rate
t = time
d = distance
therefore r * t = d is the basic equation we need.
the rabbit runs 25 feet per second and the rabbit needs to run 30 feet to get to the rabbit hole.
since r * t = d and r = 25 and d = 30, then the equation becomes 25 * t = 30 and we can solve for t to get t = 30/25 seconds.
the coyote can run 50 feet per second.
in order to get to the rabbit before the rabbit reaches its hole, the coyote needs to catch the rabbit in less than 30/25 seconds.
the equation of r * t = d for the coyote becomes 50 * 30/25 = d
we solve for d to get d = 60 feet.
if the coyote is exactly 60 feet away from the rabbit hole, the coyote will reach the rabbit just as the rabbit reaches the rabbit hole.
this will not be in time so the coyote needs to reach the rabbit before the rabbit reaches the rabbit hole.
this means the coyote has to be less than 60 feet from the rabbit hole.
we'll assume that 2 feet less is enough to allow the coyote to catch the rabbit.
this means the coyote has to be 58 feet away from the rabbit hole in order to catch the rabbit.
so, the coyote is 58 feet away from the rabbit hole and starts running towards the rabbit.
since r * t = d, the equation for the coyote becomes 50 * t = 58.
solving for t, we get t = 58/50 seconds which reduces to 29/25 seconds.
29/25 seconds is less than 30/25 seconds.
the rabbit doesn't have enough time to get to the rabbit hole and is caught.
this assumes that the rabbit hole and the rabbit and the coyote are all on the ame straight line path from the rabbit hole.
any deviation from the same completely straight path for any of them changes the assumptions of the problem which will upset the equations used rendering them useless.
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