Question

From the station, a train traveled due east while another train traveled due north. they traveled the same distance before they reached their next stations. when they stopped, they were 100 miles apart. how far did each train travel?

Answer 1

Using the Pythagorean theorem, it is determined that each train traveled approximately 70.71 miles before stopping, with each train traveling the same distance in perpendicular directions.

Step-by-step explanation:

The theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Let the distance traveled by each train be x miles. The eastward and northward travels can be considered as two sides of a right-angled triangle, with the distance between the trains (100 miles) being the hypotenuse. Using Pythagorean theorem:

x2 + x2 = 1002

This simplifies to:

2x2 = 10,000

Divide both sides by 2:

x2 = 5,000

Take the square root of both sides:

x = √5,000

x ≈ 70.71 miles

Therefore, each train traveled approximately 70.71 miles.

Answer 2

is this on ttm? or is this actual word problems.