A puppy eats a sausage 5 seconds faster than a kitten eats a identical sausage. If they share one sausage, they can eat it in 6 seconds. How long does it take each animal to eat a sausage alone?
It takes puppy ___ seconds, and it takes kitty ____ seconds.
Don't worry guys I got u the puppy takes 10 seconds and the kitty 15 seconds. oobleck just say the answer!!!!!
It takes the puppy "I'm too excited, I can't wait!" seconds, and it takes the kitty "I'll take my time, thank you" seconds.
Let's assume that the time it takes for the kitten to eat the sausage is represented by x seconds.
Since the puppy eats the sausage 5 seconds faster than the kitten, the time it takes for the puppy to eat the sausage is x - 5 seconds.
When they share one sausage, they can eat it in 6 seconds. Therefore, the equation representing the time it takes for them to eat the sausage together is:
1/x + 1/(x - 5) = 1/6
To solve this equation, we can multiply both sides by 6x(x - 5) to eliminate the fractions:
6(x - 5) + 6x = x(x - 5)
Expanding and simplifying:
6x - 30 + 6x = x^2 - 5x
12x - 30 = x^2 - 5x
Rearranging the equation:
x^2 - 17x + 30 = 0
Factoring this quadratic equation:
(x - 2)(x - 15) = 0
Setting each factor equal to zero:
x - 2 = 0 or x - 15 = 0
Solving for x:
x = 2 or x = 15
Since time cannot be negative, we discard the solution x = 15.
Therefore, it takes the kitten 2 seconds to eat the sausage alone.
To find the time it takes for the puppy, we substitute the value of x into the equation x - 5:
x - 5 = 2 - 5 = -3
Since time cannot be negative, we discard this solution as well.
Therefore, there is no valid solution for the time it takes the puppy to eat the sausage alone.
To solve this problem, let's assume that the time it takes the kitten to eat a sausage is x seconds.
Since the puppy eats a sausage 5 seconds faster than the kitten, we can say that the puppy takes (x - 5) seconds to eat the same sausage.
When they share one sausage, they can eat it in 6 seconds. This means that the combined rate of eating for both the puppy and the kitten is 1/6 sausages per second.
To break it down, we can say that the puppy's rate of eating is 1/(x-5) in sausages per second, and the kitten's rate of eating is 1/x in sausages per second.
Adding up their rates of eating gives us:
1/(x-5) + 1/x = 1/6
To find x, let's simplify the equation. We'll first multiply both sides of the equation by the least common multiple of (x-5) and x, which is x(x-5):
x(x-5) * (1/(x-5) + 1/x) = x(x-5) * (1/6)
This simplifies to:
x + (x-5) = (x(x-5))/6
2x - 5 = (x^2 - 5x)/6
To further simplify, we multiply both sides by 6 to remove the fraction:
12x - 30 = x^2 - 5x
Rearranging the equation:
0 = x^2 - 17x + 30
We can now factorize this quadratic equation:
0 = (x - 2)(x - 15)
Setting each factor equal to zero gives us two possible solutions:
x - 2 = 0 --> x = 2
x - 15 = 0 --> x = 15
Since the time it takes to eat a sausage cannot be negative, we discard the solution x = 15.
Therefore, the time it takes the kitten to eat a sausage alone is x = 2 seconds, and the time it takes the puppy to eat a sausage alone is (x - 5) = 2 - 5 = -3 seconds.
However, we cannot have a negative time, so it doesn't make sense in this context. Therefore, there is no valid solution to this problem.
If the puppy eats it in x seconds, then
1/x + 1/(x+5) = 1/6