There are two machines that produce aluminum cans. The newer machine can produce 7200 cans in 200 minutes. It takes the older machine 300 minutes to produce that many cans. If the two machines work together, how long will it take them to produce 7200 cans?
i did
200x+300x = 7200
500x=7200
x=14.4mins?
rate of newer machine =7200/200 can/min
= 36 cans/min
rate of older machine = 7200/300 cans/min
= 24 cans/min
so combined rate = 36+24 = 60 cans/min
so time for combined work = 7200/60 = 120 minutes.
Well, it seems like you've got the math right, but let's break it down with a touch of humor.
So we have two machines, one old and one new. The newer machine can pump out 7200 cans in 200 minutes, while the older machine takes a little longer at 300 minutes.
Now, if these two machines were on a playdate and decided to team up, how long would it take them to produce 7200 cans together?
To find out, we add the individual times it takes for each machine to make 7200 cans.
And when we crunch the numbers, we get 500 times "x" equals 7200. So, after some math magic, we find that "x" is equal to 14.4 minutes.
So, ding, ding, ding! You got it right! It'll take these two machines approximately 14.4 minutes to churn out 7200 shiny aluminum cans as a dynamic duo. Keep up the good work!
To solve this problem, you correctly started by setting up the equation:
200x + 300x = 7200
Combining like terms, we have:
500x = 7200
Now, let's solve for x by dividing both sides of the equation by 500:
x = 7200 / 500
Evaluating the division, we find:
x = 14.4
This means that it would take 14.4 minutes for the two machines to produce 7200 cans when working together.
To find out how long it will take the two machines to produce 7200 cans when working together, you need to set up an equation based on their individual production rates.
Let's assume the production rate of the newer machine is represented by 'x', which means it can produce x cans per minute. Since the newer machine produces 7200 cans in 200 minutes, we can set up the equation:
x * 200 = 7200
Simplifying this equation gives us:
200x = 7200
Now, let's find the production rate of the older machine. We know that it takes 300 minutes for the older machine to produce 7200 cans. So, we can set up another equation:
x * 300 = 7200
To get the combined production rate when the two machines work together, we need to add up their individual rates:
x + x = 2x
Now, let's combine the two equations we formed earlier:
200x + 300x = 7200
Simplifying:
500x = 7200
Divide both sides of the equation by 500:
x = 7200 / 500
x ≈ 14.4
Therefore, the production rate of the machines when they work together is approximately 14.4 cans per minute. Now we can find the time it takes to produce 7200 cans:
Time = Total cans / Combined production rate
Time = 7200 / 14.4
Time ≈ 500 minutes
So, when the newer and older machines work together, it will take them approximately 500 minutes to produce 7200 cans.