One printing press can print 5,000 advertising cards in 12 seconds. Another printing press can print the same number of cards in 7 1 2 seconds. If both presses are used together to print the 5,000 cards, how many seconds will it take them?
same with this one but i tried an ide and got 54 second is this right if not can you show solution
first one 5000/12 cards/s
second one 5000/7.5cards/s
together (5000/12 + 5000/7.5) cards/s
so
(5000/12 + 5000/7.5) t = 5000 cards
(1/12 + 1/7.5) t = 1
.217 t = 1
t = 4.62 seconds
clearly they do NOT take more time working together than either takes alone so it HAS to be less than 7.5 seconds.
To find the time it takes for both presses to print 5,000 cards together, we need to determine the combined rate at which they print.
Let's find the rate at which each press prints:
- The first press prints 5,000 cards in 12 seconds. Therefore, its rate is 5,000 cards / 12 seconds = 416.67 cards per second.
- The second press prints 5,000 cards in 7.5 seconds (7 1/2 = 15/2). So, its rate is 5,000 cards / 7.5 seconds = 666.67 cards per second.
To determine the combined rate, we add their rates together:
416.67 cards per second + 666.67 cards per second = 1,083.34 cards per second.
Now, let's calculate the time it takes to print 5,000 cards using the combined rate. We can use the formula: time = quantity / rate.
time = 5,000 cards / 1,083.34 cards per second ≈ 4.62 seconds.
Therefore, it would take approximately 4.62 seconds for both presses to print the 5,000 advertising cards when used together.
Regarding your calculation of 54 seconds, it seems to be incorrect. The correct answer is approximately 4.62 seconds.
To solve this problem, we can use the concept of rate and time. Let's find the time it takes for each printing press to print 5,000 cards individually first.
The first printing press can print 5,000 cards in 12 seconds, so its rate is 5,000 cards / 12 seconds = 416.67 cards per second.
The second printing press can print 5,000 cards in 7 1/2 seconds, which can be converted to a decimal as 7.5 seconds. So its rate is 5,000 cards / 7.5 seconds = 666.67 cards per second.
Now, to find the combined rate of both printing presses, we can add their individual rates: 416.67 cards per second + 666.67 cards per second = 1,083.34 cards per second.
Since we want to know how long it takes to print 5,000 cards, we can divide the number of cards by the combined rate: 5,000 cards / 1,083.34 cards per second = 4.62 seconds (rounded to two decimal places).
Therefore, it will take approximately 4.62 seconds for both printing presses to print 5,000 cards when used together.
Regarding your answer of 54 seconds, it seems like there might have been an error in the calculation. By following the steps above, you should arrive at the correct answer of approximately 4.62 seconds.