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A fox sees a rabbit 35 feet away and starts chasing it. As soon as the fox starts moving the rabbit sees it and starts running away at a speed of 40 feet per second.What should the fox's speed be to catch up to the rabbit in no more than 10 seconds?

User Jktress
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Answer: 43.5 feet per second

Step-by-step explanation: So the fox has a total of ten seconds to completely catch up with the rabbit. But how fast does he need to go.

First we need to model the distance the rabbit will travel with the equation

x = 40 * 10 + 35

x is the distance the rabbit travels, 40 is the feet per second the rabbit travels at, 10 is the number of seconds, and 35 is the distance the rabbit was away already. To figure out how fast the fox needs to travel, we need to create an equation that is equal to the answer of this one. The equation equals a total of 435. So in ten seconds, the fox needs to travel 435 feet.

Well, now that we know how many feet are required to travel to catch up to the bunny, and how many seconds, we can model it using

435 = 10 * x

x is the feet per second

To solve this equation we isolate the variable by dividing 10 on both sides

435 / 10 and 10 * x / 10, this gives us 43.5 and x or 43.5 = x

so it will take a speed of 43.5 feet per second to catch up to the rabbit.

User Mike Vierwind
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