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?

After t minutes, the positions are (if P=(0,0))

turtle: (0,4t)
snail: (50,-2t)

So, the distance d can be found from

d^2 = 50^2 + (6t)^2

Well, it sounds like we have a classic race between a speedy turtle and a sluggish snail! Let's crunch some numbers, shall we?

The turtle starts moving north at a rate of 4 feet per minute. After 5 minutes, it will have covered a distance of 4 feet/min * 5 min = 20 feet.

Meanwhile, the snail starts moving south at a rate of 2 feet per minute from a point 50 feet due east of the starting point. Since it's moving in a direct line towards the turtle, it's basically covering the horizontal distance between them. In 5 minutes, the snail will have moved 2 feet/min * 5 min = 10 feet south.

So, the distance between the two critters after 5 minutes will be the sum of the distance covered by the turtle and the distance covered by the snail. In this case, it would be 20 feet + 10 feet = 30 feet.

Therefore, after 5 minutes, the turtle and snail will be 30 feet apart. Happy racing!

To find the distance between the two animals after five minutes, we need to calculate the distance traveled by each animal.

The turtle starts moving north at a speed of 4 feet per minute for five minutes, so the distance traveled by the turtle is 4 feet/minute * 5 minutes = 20 feet.

The snail starts moving south at a speed of 2 feet per minute for five minutes, so the distance traveled by the snail is 2 feet/minute * 5 minutes = 10 feet.

Since the snail starts 50 feet due east of the point where the turtle started, we can consider the movement of the snail as a horizontal movement.

Therefore, the distance between the turtle and the snail after five minutes is the hypotenuse of a right-angled triangle with legs of 20 feet (distance traveled by the turtle) and 50 feet (initial distance between the snail and the turtle).

Using the Pythagorean theorem, we can calculate the distance between the two animals:

Distance^2 = (Leg1)^2 + (Leg2)^2
Distance^2 = 20^2 + 50^2
Distance^2 = 400 + 2500
Distance^2 = 2900

By taking the square root of both sides, we find:

Distance = √2900
Distance ≈ 53.85 feet

Therefore, the distance between the turtle and the snail five minutes after the snail starts moving is approximately 53.85 feet.

To find the distance between the two animals five minutes after the snail starts moving, we need to calculate the distance traveled by each animal during this time.

Let's break down the information given:
- The turtle starts moving north at a speed of 4 feet per minute from a point P.
- Five minutes later, the snail starts moving south at a speed of 2 feet per minute from a point 50 feet due east of P.

Since the turtle has a constant speed of 4 feet per minute for the entire duration, it would have traveled 4 feet/min * 5 min = 20 feet in those five minutes. It moves directly north from point P.

For the snail, it starts 50 feet due east of point P and moves south at a speed of 2 feet per minute. As the snail moves south, the distance between the animals decreases. This distance is a right triangle, with the hypotenuse being the total distance between the two animals.

To solve this, we need to find the length of the hypotenuse using the Pythagorean theorem. The two legs of the right triangle are the distance traveled by the turtle (20 feet) and the distance traveled by the snail (2 feet/min * 5 min = 10 feet).

Using the Pythagorean theorem:
Hypotenuse^2 = 20^2 + 10^2
Hypotenuse^2 = 400 + 100
Hypotenuse^2 = 500

Taking the square root of both sides:
Hypotenuse = √500
Hypotenuse ≈ 22.36 feet

Therefore, the distance between the two animals five minutes after the snail starts moving is approximately 22.36 feet.