Nancy can do a typing job in 8hours. When Carole helps her, they can do the job together in 5hours. How many hours would it take Carole to do the job alone?

Question

 I want to know how many hours and minutes the answer will be.

Answer 1

In 5 hours Nancy does 5/8 of the job.

In 5 hours Carole does 5/n of the job

 

5/8 + 5/n = 1

5n + 40 = 8n        multiply both sides by LCD

40 = 3n                 subtract 5n from both sides

13 1/3 = n            divide both sides by 3

 

Carole needs 13 hours 20 minutes to do the job alone.

Answer 2

Nancy's rate is 1 job per 8 hours = 1/8 job/hr

Carole's rate is 1 job per 'n' hours = 1/n job/hr

 

Together's rate is 1 job per 5 hours = 1/5 job/hr

 

So just adding the rates, you'll get:

 

1/8 + 1/n = 1/5

 

n = 40/3 or 13.33 hrs

 

*The key here is that you are adding the rates. Neither the job nor the time alone. THE RATES.*

Answer 3

The formula for these types of problems is the following:

 

   time together           +      time together      =  1      

Nancy's time alone         Carole's time alone

 

Let x = the time it would take Carole alone

 

5  +  5  = 1         Multiply both sides by 8x.

8      x

 

5x + 40 = 8x

        40 = 3x

 13 1/3 = x       Since 1/3 of an hour = 1/3(60) = 20,

                           it takes Carole 13 hours and 20 minutes to do

                           the job alone.