Hard math question -- I think
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Hard math question -- I think

[From: ] [author: ] [Date: 12-05-01] [Hit: ]
They start out 1/4 mile apart. At what point will the Lion overtake the Zebra?Thanks!-Well, first of all lets set the starting point of the lion equal to 0 on a number line. That means,......
This seems hard to me. Maybe easy but I sure need help. Just the setup -- not the answer, unless you want to also provide the answer. Here's the question:

A lion runs 50 MPH and a Zebra runs 40MPH. They start out 1/4 mile apart. At what point will the Lion overtake the Zebra?

Thanks!

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Well, first of all let's set the starting point of the lion equal to 0 on a number line. That means, the zebra starts at 1/4. Set x equal to the point where the lion overtakes the zebra.

The total distance the lion has to run to overtake the zebra is x. The total distance the zebra has to run is x - 1/4.

We know that speed = (distance) / (time) or time = (distance) / (speed)
When they are at point x, the same amount of time passed.
Therefore, we can set time equal.

Distance traveled by lion / speed of lion = Distance traveled by zebra = speed of zebra
x / 50 = (x - 1/4) / 40
Solving for x, you get x=5/4

So the lion overtakes the zebra at a point 5/4 miles from where the lion started out (or a mile away from where the zebra did).

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Speed of lion = 50 mph
Speed of zebra = 40 mph
Closing speed = 50 mph - 40 mph (10mph)
Time = h

Closing distance = relative speed x time
.25 miles = 10 mph x total hours

Go get'em lion!

EDIT: "At what point" can refer to distance and/or time.
The formula above will enable you to determine how long it will take for the lion to overtake the zebra. If you do the right calculations, you'll discover that the lion will be feasting on zebra in 90 seconds. You can calculate the distance covered afterward if you want to.

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If the L and Z start running towards each other at the same, then the time, t where they meet will be the same :-)

If L ran the distance, d then Z ran the distance (1/4) - d

speed = distance / time or time = distance / speed
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