Jena and Cindy, Working together can clean the house in 10 hours. Working alone, cindy takes twice as long as jena. How longs does it take jena to clean the house.
Let Jena time alone be x hrs
let Cindy's time alone be 2x hrs
let the two rates be
1/x and 1/(2x)
combined rate = 1/x + 1/(2x) = 3/(2x)
1/(3/(2x)) = 10
2x/3 = 10 hrs =
2x = 30 or x = 15
Jena will take 15 hrs to do the house alone
Let's say Jena takes x hours to clean the house alone. According to the given information, Cindy takes twice as long as Jena, so Cindy takes 2x hours to clean the house alone.
When Jena and Cindy work together, their combined rate of cleaning is 1/10 of the house per hour since they complete the whole house in 10 hours.
To find their individual rates, we can set up the equation:
1/x + 1/(2x) = 1/10
Now, let's solve the equation step-by-step to find x:
First, we can simplify the equation by finding a common denominator:
(2 + 1)/(2x) = 1/10
3/(2x) = 1/10
Cross-multiplying, we get:
3 * 10 = 2x
30 = 2x
Dividing both sides by 2, we get:
x = 30/2
x = 15
Therefore, it takes Jena 15 hours to clean the house alone.
To solve this problem, we can assign variables to represent the time it takes for Jena and Cindy to clean the house alone.
Let's say Jena takes 'x' hours to clean the house alone. Since Cindy takes twice as long as Jena, we can say Cindy takes '2x' hours to clean the house alone.
According to the information given, when working together, Jena and Cindy can clean the house in 10 hours.
Working together, Jena and Cindy's combined work rate is the sum of their individual work rates. Hence, we can set up the equation:
1/x + 1/2x = 1/10
Multiplying every term by 10x to eliminate the denominators, we get:
10 + 5 = x
Simplifying further:
15 = x
Therefore, it takes Jena 15 hours to clean the house alone.