Kinetic energy of two different masses (ratio)

[alingy1]

Homework Statement

Two masses, one of 20kg and the other of 40kg, are pushed using the same force on the same distance.
What is the ratio of the kinetic energy? (Kinetic energy of 20kg/kinetic energy of 40kg)

Homework Equations

Ek=mv^2
F=ma
v=at

The Attempt at a Solution

So, I found that the answer is 2/1. But the answer key says it's 1/1.
Here's my logic:
Let's say the constant force is 20N.
And that the time the force is applied is 3 seconds.

20kg:
F=ma
a=1m/s^2
v=3m/s
Ek=mv^2/2=90N

40kg:
F=ma
a=0,5m/s^2
v=1,5m/s
Ek=mv^2/2=45N

Ratio: 90/45=2/1

Why does the answer key say otherwise? Is my logic false somewhere? Please help. My exam is coming up soon.

 

[FBayer]

The error is in that you're using the wrong formulae and making up arbitrary values.

The formula to be used here is W = Fd (work = force × distance). Work is the same concept as energy. If you use that, you can see that the energy is the same for both, because if the Force and the distance are both the same, the work done on the masses (= their kinetic energy) must be the same as well.

Also, your units are wrong – energy is measured in Joules (J), not Newtons (N).

 

[consciousness]

The problem says over the same distance not the same time. Anyway its not a good idea to assume values of anything.
What is definition of work? Do you know the work energy theorem?