Question

Combined, two production lines can make 315 light bulbs in 1 hour. Production line A produces light bulbs 1.1 times faster than production line B. Using a rational equation, which of the following correctly calculates how many light bulbs can be produced in 1 hour using only production line A?

Answer 1

Let's define the production rates of the two lines.

Let \( r_B \) be the rate at which production line B produces light bulbs per hour. Then, since production line A produces light bulbs 1.1 times faster than production line B, we can express the rate of production line A as:

\[
r_A = 1.1 r_B
\]

The combined production of both lines is given as 315 light bulbs per hour:

\[
r_A + r_B = 315
\]

Now, substituting for \( r_A \):

\[
1.1 r_B + r_B = 315
\]

Combine the terms on the left-hand side:

\[
2.1 r_B = 315
\]

Now, we can solve for \( r_B \):

\[
r_B = \frac{315}{2.1}
\]

Calculating this gives:

\[
r_B = 150
\]

Now we want to find the production rate for production line A, which is:

\[
r_A = 1.1 r_B = 1.1 \times 150 = 165
\]

So, production line A can produce **165 light bulbs in 1 hour**.

To summarize, the correct rational equation based on the problem's conditions is:

\[
r_A = 315 - r_B
\]

And substituting in our earlier expression gives the solution that:

\[
r_A = 1.1 \cdot \left( \frac{315}{2.1} \right)
\]

This shows that production line A can produce **165 light bulbs** in **1 hour**.