Question

How Do You Find A Train? (Math Riddle)

A. By solving the equation x + 5 = 10 for x.
B. By calculating the area of a circle with radius 5.
C. By finding the square root of 100.
D. By multiplying 2 by 3.

Answer 1

To find the distance a train has moved, use the equation x = rθ where x is the distance, r is the wheel radius, and θ is the angle in radians. Substitute known values into the equation and check the reasonableness of the result.

Step-by-step explanation:

To find the distance a train moved down the track, you need to use the equation x = rθ, where x is the distance, r is the radius of the wheel of the train, and θ is the angle in radians that the wheel has rotated. The steps to solve this riddle include:

1. Identify the known values: the radius (r) and the angle of rotation (θ).
2. Solve the equation for the unknown value, which in this case is the distance (x).
3. Substitute the known values into the equation, ensuring you use the correct units, especially for the angle (θ), which should be in radians.
4. Check that your answer is reasonable in terms of units and magnitude.

In our case, substituting the known values would give us: x = (0.350 m)(1257 rad) = 440 m.

The number of revolutions (200 rev) is converted to radians using the fact that one revolution is equal to 2π radians. This gives us θ = (200 rev) ⋅ (2π rad/rev) = 1257 rad.