Replace the three loads with a single load Give the distance

Replace the three loads with a single load. Give the distance from the left support. a. 11.2 ft b. 9.21ft c. 6 89 ft d. 417ft e. 8.67ft

Let Ra and Rb be the reactions at left and right hinges respectively.

By moment balance at left hinge: (As we know M = R X F )

45*3 + 35*7 + 55*10 = Rb*12

Solving this we get , Rb = 77.5lb

Sum total of all the forces = 45 + 35 + 55 = 135lb

Let the distacnce of single load from left hinge is \"d\"

So again doing moment balace at left hinge we get,

135*d = 77.5*12

solving we get d = 6.89ft which is option (c) here.