Question 288255: Okay, here goes another easy one that I can't solve:
Printer A can print a report in 3 hours.
Printer B can print a report in 4 hours.
How long would it take for both printers, working together, to print the report?
I've used several different formulas and can answer the practice questions correctly, but I'm not sure HOW I'm answering them correctly, because I don't understand why I'm using this formula.
Last attempt I used:
t over 4 plus t over 3 = 1 report
t over 4 multiplied by 3 = 3t over 12
t over 3 multiplied by 4 = 4t over 12
3t plus 4t over 12 = 7t over 12
so, 7t over 12 = 1 report.
I multiply each side by 12 (this is where I start to wonder what I'm doing...)
So I have 84t over 12 = 12 or I have 7t = 12,
which results in:
t = 1 and 5 over 7.
Can this possibly be right?
If so, why did I multiply each side by 12 or was I supposed to divide before dividing again?
I understand the problem in the book, but it uses 3 and 6 and I've tried several different ways,
but they all come up with the correct answer of "2", so I don't know which formula is correct or why I keep getting the right answer even though I don't know what I'm doing.
Any help or explanation is greatly appreciated, thank you!
Answer by amnd(23)   (Show Source):
You can put this solution on YOUR website! I don't see what you're doing wrong. I got the same answer (12/7, or 1 and 5/7) through a similar method:
.
Rate of A: 1/3
Rate of B: 1/4
Time working together: x
.
The equation would then be:
x/3 + x/4 = 1
(4x + 3x)/12=1
7x=12
x=12/7
.
You multiplied both sides to get rid of the divisor (12), I assume... Although I think an easier way would've been to simply move 12 to the expression on the right of the equation, turning the divisor into a multiplier (as I have done).
.
You might want to consider the possibility of the book rounding up the answer to the nearest hour (which is indeed "2"). Hope this helps.
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