A turtle starts moving north at
4 feet per minute from a point P.
Five minutes later,
a snail starts moving south at 2 feet per minute from a point 50 feet due east of P.
What is the distance
(in feet) between the two animals five minutes after the snail starts moving?
To find the distance between the turtle and snail five minutes after the snail starts moving, we need to calculate the distance traveled by each animal during this time.
Let's start with the turtle. The turtle moves north at a rate of 4 feet per minute. Since it started moving five minutes before the snail, the turtle will have traveled 4 feet per minute multiplied by 5 minutes, which equals 20 feet north of point P.
Next, let's calculate the distance traveled by the snail. The snail moves south at a rate of 2 feet per minute. Since it started moving later than the turtle, we need to account for the snail's starting position. The snail starts 50 feet due east of point P, and it moves south from there. Since the snail travels for 5 minutes, the distance traveled by the snail will be 2 feet per minute multiplied by 5 minutes, which equals 10 feet south.
Now, we can calculate the distance between the two animals. From the turtle's position, we measure the straight-line distance to the snail's position. We can assume this distance forms a right-angled triangle, with one leg being the turtle's position (20 feet north) and the other leg being the snail's position (10 feet south).
Using the Pythagorean theorem, we can find the length of the hypotenuse, which represents the distance between the turtle and snail. The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the hypotenuse is the distance we want to find, the north leg of the triangle is 20 feet, and the south leg is 10 feet.
Hence, using the Pythagorean theorem:
Hypotenuse^2 = North leg^2 + South leg^2
Hypotenuse^2 = 20^2 + 10^2
Hypotenuse^2 = 400 + 100
Hypotenuse^2 = 500
To find the hypotenuse, we take the square root of both sides:
Hypotenuse = sqrt(500) ≈ 22.36 feet
Therefore, the distance between the turtle and snail five minutes after the snail starts moving is approximately 22.36 feet.