Two lifeguards pull on ropes attached to a

Question

raft. If they pull in the same direction, the raft
experiences a net external force of 332 N to
the right. If they pull in opposite directions,
the raft experiences a net external force of
122 N to the left.
Draw a free body diagramfor each situation
and find the magnitude of the larger of the two
individual forces.
Answer in units of N

Answer 1

Resolve forces into x,y components.
Let the x-components of forces be f1,f2
then
f1+f2=332
f1-f2=122

Solving
f1=(332+122)/2=227
f2=(332-122)/2=105
Assuming θ=0 (in direction of raft)
so the forces are 227 and 105N