Question

In this fulcrum, for the weights to be balance, what do the distances d1 and d2 have to be if the overall length is 12 feet?

D1= 6.55 ft./ 5.45 ft./ 7.20 ft.
D2= 5.45 ft./ 6.55 ft./ 4.80 ft.

Answer 1

For this case we have the following system of equations:
Equilibrium equation:
60 * d1 = 50 * d2
Total distance:
d1 + d2 = 12
Solving the equations we have:
d1 = 5.45 feet
d2 = 6.55 feet
Answer:
the distances d1 and d2 have to be:
d1 = 5.45 feet
d2 = 6.55 feet

Answer 2

For the fulcrum to balance, the product of weight and distance on both sides of the fulcrum must be the same.

Let d1= x. since total distance is 12, we can write d2 = 12 - x

for the fulcrum to balance:

60x = 50(12 - x)

60x = 600 - 50x

110x = 600

x = 5.45

Thus, d1= 5.45
and
d2= 12 - d1 = 12 - 5.45 = 6.55

d1 = 5.45
d2 = 6.55