To solve the problem, we need to define the production rates of both production lines A and B in order to set up a rational equation.
Let the production rate of line B be \( x \) light bulbs per hour. Since production line A produces light bulbs 1.1 times faster than line B, the production rate of line A would be \( 1.1x \).
Combined, the two production lines can produce 315 light bulbs in 1 hour. Therefore, we can set up the following equation:
\[ x + 1.1x = 315 \]
Now, we can combine like terms:
\[ 2.1x = 315 \]
To solve for \( x \), divide by 2.1:
\[ x = \frac{315}{2.1} \]
Calculating \( x \):
\[ x = 150 \quad \text{(this is the production rate of line B)} \]
Now we can calculate the production rate of line A:
\[ 1.1x = 1.1 \times 150 = 165 \quad \text{(this is the production rate of line A)} \]
Thus, production line A can produce 165 light bulbs in 1 hour.
So, the rational equation which calculates how many light bulbs can be produced using only production line A is:
\[ 1.1x = 165 \]
Therefore, using production line A only, it can produce 165 light bulbs in 1 hour.
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