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 hours using only production line A?
Let's say the number of light bulbs produced by production line B in 1 hour is x.
Then the number of light bulbs produced by production line A in 1 hour is 1.1x (as it is 1.1 times faster than line B).
The combined production of both lines is given as 315 light bulbs in 1 hour.
So, we can write the equation as: x + 1.1x = 315.
Combining like terms, we get: 2.1x = 315.
Dividing both sides of the equation by 2.1, we get: x = 315 / 2.1.
Simplifying, we find that x = 150.
Therefore, production line B can produce 150 light bulbs in 1 hour.
Since production line A produces light bulbs 1.1 times faster than line B, it can produce 1.1 * 150 = 165 light bulbs in 1 hour.
Therefore, the correct equation would be x + (1.1x) = 315, which can be simplified as 2.1x = 315.
Let's assume that the rate of production for production line B is x light bulbs per hour.
Since production line A produces light bulbs 1.1 times faster than production line B, the rate of production for production line A is 1.1x light bulbs per hour.
To find the total number of light bulbs that can be produced using both production lines in 1 hour, we can add their rates of production:
x + 1.1x = 315
Combining like terms, we have:
2.1x = 315
To solve for x, we divide both sides of the equation by 2.1:
x = 315/2.1
Simplifying, x = 150
So, production line B can produce 150 light bulbs in 1 hour.
Now, let's calculate how many light bulbs can be produced in 1 hour using only production line A. Since production line A produces light bulbs 1.1 times faster than production line B, the rate of production for production line A is 1.1 * 150 = 165 light bulbs per hour.
Therefore, production line A can produce 165 light bulbs in 1 hour.
To solve this problem using a rational equation, let's first set up the equations for both production lines:
Let's assume that production line B produces x light bulbs in 1 hour.
Therefore, production line A produces 1.1x light bulbs in 1 hour since it produces light bulbs 1.1 times faster than line B.
Now, we can combine the production rates of both lines:
The combined production rate is the sum of the production rates of line A and line B, which is equal to 315 light bulbs per hour.
So, we can express this as an equation:
1.1x + x = 315
Since we want to find the number of light bulbs produced by line A in 1 hour, which is 1.1x, we can solve this equation.
First, combine like terms:
2.1x = 315
Next, divide both sides of the equation by 2.1 to isolate x:
x = 315 / 2.1
Calculating this, we get:
x ≈ 150
So, line B can produce approximately 150 light bulbs in 1 hour.
Now, to find the number of light bulbs produced by line A in 1 hour, we multiply the production rate of line B by 1.1:
1.1 * 150 = 165
Therefore, line A can produce approximately 165 light bulbs in 1 hour.
Thus, the correct rational equation for the number of light bulbs produced by line A in 1 hour is:
1.1x, where x is the number of light bulbs produced by line B.