Mary and John are on opposite sides of a seesaw. Mary has 3x the mass of John. If Mary is sitting at a distance of .5m from the fulcrum, how far must John site in order to keep it balanced.

John's mass = x kg,

Mary's mass = 3x kg,
3x * 0.5 = x * d,
Solve for d by dividing both sides by x:

d = 3 * 0.5 = 1.5 m.

To find the distance John must sit in order to keep the seesaw balanced, we can use the principle of moments. The principle of moments states that the total anticlockwise moment is equal to the total clockwise moment.

In this case, the moment is the product of the mass and the distance from the fulcrum. Let's assume the mass of John is "m" and the mass of Mary is "3m".

Using the principle of moments, we can write:

(Moment of Mary) = (Moment of John)
(3m) * (0.5m) = (m) * (x)

Simplifying this equation, we get:

1.5m = mx

Solving for x, we divide both sides of the equation by m:

x = 1.5

Therefore, John must sit at a distance of 1.5 meters from the fulcrum in order to keep the seesaw balanced.

To answer this question, we need to consider the lever arm principle, which states that in order for a seesaw to be balanced, the torque on one side must be equal to the torque on the other side.

Torque is calculated by multiplying the force applied to an object by the distance from the pivot point (fulcrum in this case). In this situation, the force being applied is the weight of each person, which is equal to their respective mass multiplied by the acceleration due to gravity (9.8 m/s^2).

Let's denote the mass of John as "m" and the mass of Mary as "3m" (since Mary has 3 times the mass of John). The distance from the fulcrum at which Mary sits is 0.5m.

Torque on Mary's side: Torque_Mary = (3m) * (0.5m) * (9.8 m/s^2)
Torque on John's side: Torque_John = m * (x) * (9.8 m/s^2)

Since the seesaw is balanced, the torques must be equal:
(3m) * (0.5m) * (9.8 m/s^2) = m * (x) * (9.8 m/s^2)

Simplifying the equation, we get:
(3/2) * (9.8 m/s^2) = x * (9.8 m/s^2)

Canceling out the acceleration due to gravity, we find:
(3/2) = x

So, John must sit at a distance of 1.5m from the fulcrum in order to keep the seesaw balanced.