Newton's Second Law Equation acceleration Question

[Slusho]

Homework Statement

A certain force gives object m₁ an acceleration of 12.0 m/s². The same force gives object m₂ an acceleration of 3.30 m/s². What acceleration would the force give to an object whose mass is (a) the difference between m₁ and m₂ and (b) the sum of m₁ and m₂.

Homework Equations

F=ma

The Attempt at a Solution

I found these two solutions online:
http://www.physforum.com/index.php?showtopic=6754
http://www.jiskha.com/display.cgi?id=1286634662
but I can't follow their math. I tried manipulating the above equation similarly, to no avail.

Any help is greatly appreciated!

 

[azizlwl]

Which part that you do not understand.
Use the formula a=F/m.

 

[SammyS]

Homework Statement

A certain force gives object m₁ an acceleration of 12.0 m/s². The same force gives object m₂ an acceleration of 3.30 m/s². What acceleration would the force give to an object whose mass is (a) the difference between m₁ and m₂ and (b) the sum of m₁ and m₂.

Homework Equations

F=ma

The Attempt at a Solution

I found these two solutions online:
http://www.physforum.com/index.php?showtopic=6754
http://www.jiskha.com/display.cgi?id=1286634662
but I can't follow their math. I tried manipulating the above equation similarly, to no avail.

Any help is greatly appreciated!

Hello Slusho. Welcome to PF !

What are those manipulations? What have you tried?

F = m₁a₁ and F = m₂a₂, where a₁ = 12.0 m/s² and a₂ = 3.30 m/s² .

Therefore, $\displaystyle m_1=\frac{F}{a_1}\text{ and } m_2=\frac{F}{a_2}\,.$ Correct?

Now, use all this with F = (m₁ + m₂)a₁₊₂ to find a₁₊₂ .

How's your algebra?

 

[Slusho]

I figured it out!

$$F=(\frac{F}{a_{1}}+\frac{F}{a_{2}})a_{1+2}$$
$$\frac{1}{a_{1+2}}=\frac{1}{F}(\frac{F}{a_{1}}+ \frac{F}{a_{2}})$$
$$\frac{1}{a_{1+2}}=\frac{1}{a_{1}}+\frac{1}{a_{2}}$$

Thank you so much for you help! I had to work it several ways for a good half hour until I did it correctly.