Hello, Jack, thank you for the email, We all hope you are fully recovered from your illness.

This type of problem is called the motion of connected bodies.

The secret is to figure out what is connected and what additional equations can be had because of this connection.

Did you draw a diagram?

With reference to mine

Mass M1 only moves horizontally and mass M2 only moves vertically.

There is no friction anywhere so the tension is constant throughout the string. Call this T.

(Generally if friction is involved there will be different tensions in different parts of the string)

So writing Newton's Law equations for the motion Force = mass times acceleration for each particle with accelerations a1 and a2.

This allows us to substitute for the tension and eliminate it, but leaves us with a1 and a2.

Now chip has told you that a1 = 2a2.

This is easy to say, but can you prove it mathematically?

(This bit is often omitted in textbooks)

Well because the string does not stretch, break or go slack, the amount of string passing over pulley1 horizontally must be the same as the **total** amount of string that is added to both of the two support sides of the pulley2 as it descends.

So half the string is added to each side of pulley2 support so pulley2 descends vertically half the distance m1 moves horizontally.

But both m1 and m2 start from rest so at any time t from rest

s1 = 2s2.

So resorting to our old friend s = ut + 1/2 a t^2 we can show

a1 = 2 a2 as chip said.

I will leave you to finish the algebra to obtain the correct answers.