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?
1. 150 light bulbs
2. 300 light bulbs
3. 165 light bulbs
4. 158 light bulbs
Let x be the number of light bulbs produced in 1 hour using production line B.
Using the information given, production line A can produce 1.1x light bulbs in 1 hour.
Together, production line A and B can produce x + 1.1x = 2.1x light bulbs in 1 hour.
We are given that 2.1x = 315.
So, x = 315/2.1 = 150.
Therefore, production line A can produce 1.1*150 = 165 light bulbs in 1 hour.
The correct answer is option 3. 165 light bulbs.
Let's assume the number of light bulbs produced by production line B in 1 hour is "x."
According to the given information, production line A produces light bulbs 1.1 times faster than production line B. So, the number of light bulbs produced by production line A in 1 hour is 1.1x.
Combined, the two production lines can make 315 light bulbs in 1 hour. Therefore, we can set up the equation:
x + 1.1x = 315
Combining like terms, we get:
2.1x = 315
Dividing both sides of the equation by 2.1, we find:
x = 150
So, production line B can produce 150 light bulbs in 1 hour.
Now, to find how many light bulbs can be produced in 1 hour using only production line A, we substitute the value of x into the equation:
1.1x = 1.1 * 150 = 165
Therefore, the correct answer is option 3. Production line A can produce 165 light bulbs in 1 hour.
To solve this problem, let's first assign variables to represent the speeds of the two production lines. Let's say the speed of production line B is x light bulbs per hour. The speed of production line A would be 1.1 times faster than x, so the speed of production line A would be 1.1x light bulbs per hour.
Next, let's set up a rational equation to represent the total number of light bulbs produced per hour when both production lines are working together. We know that combined, the two production lines can make 315 light bulbs in 1 hour, so the equation would be:
x + 1.1x = 315
Simplifying the equation, we can combine like terms:
2.1x = 315
Now, to find the value of x (the speed of production line B), divide both sides of the equation by 2.1:
x = 315 / 2.1
Calculating this gives us:
x ≈ 150
So, the speed of production line B is approximately 150 light bulbs per hour.
Now, we can use this value to calculate how many light bulbs can be produced in 1 hour using only production line A, which is 1.1 times faster.
Production line A = 1.1 * 150 = 165
Therefore, the correct answer is option 3: 165 light bulbs can be produced in 1 hour using only production line A.