Two boats leave a dock at the same time. One heads due east at 20 mph, and one heads due south at 15 mph. How far apart are the two boats after 45 minutes have elapsed?

I wonder if there is a current assiging one in someway?

Assuming not, in 3/4 hr
one is east 15 miles, and the other is S at 45/4 miles

How far apart?
distance=sqrt(15^2 + (45/4)^2 )

Please explain (45/4)^2. One boat is headed due east at 20 mph, and one heads due south at 15 mph

To find the distance between the two boats after 45 minutes, we need to calculate the distance each boat has traveled in that time.

The boat heading due east at 20 mph will have traveled:

Distance = Speed x Time
Distance = 20 mph x (45 minutes / 60 minutes per hour)
Distance = 20 mph x (0.75 hours)
Distance = 15 miles

The boat heading due south at 15 mph will have traveled:

Distance = Speed x Time
Distance = 15 mph x (45 minutes / 60 minutes per hour)
Distance = 15 mph x (0.75 hours)
Distance = 11.25 miles

To find the distance between the two boats, we can use the Pythagorean theorem, as the boats are traveling at right angles to each other:

Distance = √(Distance1^2 + Distance2^2)
Distance = √(15^2 + 11.25^2)
Distance = √(225 + 126.5625)
Distance = √(351.5625)
Distance ≈ 18.73 miles

Therefore, the two boats will be approximately 18.73 miles apart after 45 minutes have elapsed.

To find the distance between the two boats after 45 minutes, we first need to calculate how far each boat has traveled in that time.

Boat 1 travels due east at a speed of 20 mph. Since it has been 45 minutes, we need to convert this time into hours by dividing it by 60: 45 minutes ÷ 60 minutes/hour = 0.75 hours.

So, Boat 1 has traveled 20 mph × 0.75 hours = 15 miles.

Boat 2 travels due south at a speed of 15 mph. Using the same approach, we find that Boat 2 has traveled 15 mph × 0.75 hours = 11.25 miles.

Now, we can use the Pythagorean theorem to calculate the distance between the two boats. The theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, Boat 1 has traveled east and Boat 2 has traveled south, creating a right triangle. The distance between the two boats is the hypotenuse of this triangle.

Using the distance traveled by each boat as the lengths of the triangle's legs, we have:

Hypotenuse² = (15 miles)² + (11.25 miles)²

Hypotenuse² = 225 square miles + 126.5625 square miles

Hypotenuse² = 351.5625 square miles

Now, we can find the square root of both sides to find the value of the hypotenuse:

Hypotenuse ≈ √(351.5625 square miles)

Hypotenuse ≈ 18.73 miles

Therefore, the two boats are approximately 18.73 miles apart after 45 minutes have elapsed.