Thermal Elongation of 2 different rods

[Karol]

Homework Statement

A metal rod of length 30 cm elongates 0.075 cm when heated from 0⁰C to 100⁰C. a second rod of the same length but from an other metal elongates, at the same temperature difference, 0.045 cm.
A third rod is made of 2 pieces from the 2 previous ones and of the same length elongates, at the same temperature difference, 0.06 cm. what are the length of the 2 pieces the rod is made of.

Homework Equations

$$L=L_0(1+\alpha\Delta t)$$

The Attempt at a Solution

Finding $\alpha$ of the rods:
$$30.075=30(1+100\alpha_1)\rightarrow\alpha_1=25E-6$$
$$30.045=30(1+100\alpha_2)\rightarrow\alpha_2=15E-6$$
The combined rod:
$$30.06=L_1(1+100\alpha_1)+(30-L_1)(1+100\alpha_2)$$
$$0.06=L_1(25-15)E-4+30\cdot 15E-4$$
$$0.06=L_1\cdot 10E-4+0.045\rightarrow L_1=15$$
The answer should be 10 cm and 20 cm

 

[nasu]

I think your answer is correct. But you can always check which one provides the correct elongation.

 

[Chestermiller]

I get 15 also.

Chet