Carlos and Sam together unpacked cartons
for 3 hours at a rate of 8 cartons per hour.
During that time, Carlos unpacked twice as
many cartons as Sam. How many cartons
did each of them unpack?
Let Sam's rate be x cartons/hr
then Carlos' rate would be 2x cartons/h
combined rate = 3x cartons/hr
so in 3 hours they unpacked 3(3x) cartons
so 9x = 24
x = 8/3 cartons
Sam rate is 8/3 cartons/hr, and Carlos' rate is 16/3 cartons/hr
so Sam did (8/3)(3) or 8 cartons, and Carlos did 16/3)(3) or 16 cartons
Check: their combined rate would be (8/3 + 16/3) or 8 cartons/hr
so in 3 hours they would unpack 24 cartons
my answer is correct, the bot's answer makes no sense,
The question was, how many cartons did each unpack. Not how fast they did it.
3 hours at a rate of 8 cartons per hour = 24 cartons.
So Sam did 8 and Carlos did 16.
To solve the problem, let's use algebra and define variables for the number of cartons unpacked by Carlos and Sam.
Let's say:
C = number of cartons unpacked by Carlos
S = number of cartons unpacked by Sam
From the given information, we know a few things:
1. Carlos and Sam unpacked cartons for 3 hours.
2. Their combined rate is 8 cartons per hour.
So the total number of cartons unpacked by both Carlos and Sam can be calculated as:
3 hours * 8 cartons per hour = 24 cartons
Now, since Carlos unpacked twice as many cartons as Sam, we can create an equation:
C = 2S
Substituting this equation into the total number of cartons formula, we get:
C + S = 24
Now we can substitute the value of C from the previous equation:
2S + S = 24
3S = 24
S = 24 / 3
S = 8
So Sam unpacked 8 cartons.
To find the number of cartons unpacked by Carlos, we substitute the value of S into the equation:
C = 2S
C = 2 * 8
C = 16
Therefore, Carlos unpacked 16 cartons.
In conclusion, Sam unpacked 8 cartons, and Carlos unpacked 16 cartons.