Nancy can do a typing job in 8 hours. When Carole helps her, they can do the job together in 5 hours. How many hours would it take Carole to do the job alone?
i got that carole can fo it in 13 hours and 20 minutes alone is this right?
Thanks
1/8 + 1/x = 1/5
x+8/8x = 1/5
5x+ 40 = 8x 3x = 40
x = 40/3 = 13hr 20min.
To find out how many hours it would take Carole to do the job alone, we can use the concept of work rates.
Let's say Nancy's work rate is represented by N (in jobs per hour) and Carole's work rate is represented by C (in jobs per hour).
We are given that Nancy can do the job in 8 hours, so her work rate (N) is 1/8 jobs per hour (since she can do the job in 1/8th of the total time).
When Carole helps Nancy, together they can do the job in 5 hours. So their combined work rate (N + C) is 1/5 jobs per hour.
Now, using the concept that the combined work rate is the sum of individual work rates, we can set up the equation:
N + C = 1/5
Since we already know Nancy's work rate is 1/8, we can substitute that value into the equation:
1/8 + C = 1/5
Now we can solve for C, to find Carole's work rate:
C = 1/5 - 1/8
To subtract fractions, we need a common denominator. The least common multiple of 5 and 8 is 40, so let's rewrite the equation with 40 as the common denominator:
C = 8/40 - 5/40
C = 3/40
The work rate for Carole is 3/40 jobs per hour.
To find out how many hours it would take Carole to do the job alone, we can take the reciprocal of her work rate:
1 / (3/40) = 40/3 = 13.33 hours
So, it would take Carole approximately 13 hours and 20 minutes to do the job alone.
Therefore, your calculation of Carole taking 13 hours and 20 minutes to do the job alone is correct.
correct,
how did you get that?
I am more interested in your method and thinking than the actual answer.