Leg Presses Work Energy Theorem Confusion

[ehabmozart]

Homework Statement

As part of your daily workout, you lie on
your back and push with your feet against a platform attached to
two stiff springs arranged side by side so that they are parallel to
each other. When you push the platform, you compress the springs.
You do 80.0 J of work when you compress the springs 0.200 m
from their uncompressed length. (a) What magnitude of force must
you apply to hold the platform in this position? (b) How much
additional work must you do to move the platform 0.200 m
farther, and what maximum force must you apply?

Homework Equations

Work Energy theorem ONLY!

The Attempt at a Solution

I assumed that the 80 J would be equal to the sum of work done to compress each spring... So 80 J = 2* (.5 K x^2) ... However, the book had an attempt directly the 80 J = .5 Kx^2... Kindly Clarify why is it so if the force is applied on two springs? THANKS A LOT!

 

[TSny]

Perhaps they are letting K represent the effective spring constant of both springs together. Your approach is also fine. Both methods should give the same answers for (a) and (b).