Let's denote the number of bulbs produced by production line B in one hour as \( x \). According to the problem, production line A produces bulbs 1.1 times faster than line B, so the production of line A would be \( 1.1x \).
We know that the combined production from both lines is 315 bulbs in one hour, which gives us the equation:
\[ x + 1.1x = 315 \]
This can be simplified to:
\[ 2.1x = 315 \]
Now, we can solve for \( x \):
\[ x = \frac{315}{2.1} = 150 \]
Thus, line B produces 150 bulbs in one hour. Then, we find the production of line A:
\[ 1.1x = 1.1 \cdot 150 = 165 \]
So, line A produces 165 bulbs in one hour.
Now, let's check the given options:
a) Line A can make 126 bulbs in 1 hour. (False) b) Line B can make 105 bulbs in 1 hour. (False) c) Line A can make 140 bulbs in 1 hour. (False) d) Line B can make 70 bulbs in 1 hour. (False)
None of the provided options a, b, c, or d are correct based on our calculations.
The correct production rates are:
- Line A: 165 bulbs/hour
- Line B: 150 bulbs/hour