Susie weighs 100lbs. Sam weighs 150. The seesaw is 20ft long. The seat on one side only is movable in one foot increments. At what distance from the axis should the seat be placed in order for them to balance? Where should each person sit?
To determine the position at which Susie and Sam can balance on the seesaw, we need to consider their respective weights and the distance of the seat from the axis.
Let's consider the torque on each side of the seesaw. Torque is the product of the force applied and the distance from the axis where the force is applied. In order for the seesaw to balance, the torques on both sides need to be equal.
Given that Susie weighs 100lbs and Sam weighs 150lbs, let's assume Susie sits on one side and Sam sits on the other side. If Susie sits at a distance 'x' from the axis, the torque on her side would be 100lbs * x. Similarly, if Sam sits at a distance 'y' from the axis, the torque on his side would be 150lbs * y.
To balance the seesaw, the two torques must be equal. Therefore, we have the equation:
100lbs * x = 150lbs * y
Since the length of the seesaw is 20ft, the total distance from the axis would be 20ft. Therefore, x + y = 20ft.
Now we have a system of two equations:
1. 100lbs * x = 150lbs * y
2. x + y = 20ft
We can use substitution or elimination to solve this system of equations.
Let's solve it using substitution:
From equation 2, we have x = 20ft - y
Substituting this value in equation 1, we get:
100lbs * (20ft - y) = 150lbs * y
Now, we can solve this equation:
2000lbs - 100lbs * y = 150lbs * y
2000lbs = 250lbs * y
y = 8ft
Substituting the value of y back into equation 2:
x + 8ft = 20ft
x = 12ft
So, in order for Susie and Sam to balance on the seesaw, the movable seat should be placed at a distance of 12ft from the axis. Susie should sit 12ft away from the axis, and Sam should sit 8ft away from the axis.