it takes me 10 hours to clean house. It takes jan 11 hours to clean the same house. If me an January work together, how long will it take to clean the house

Question

it takes me 10 hours to clean house. It takes jan 11 hours to clean the same house. If me an January work together, how long will it take to clean the house

Answer 1

Since it takes you 10 hours to clean the house, you clean 1/10 of the house per hour. Since it takes Jan 11 hours to clean the house, she cleans 1/11 of the house per hour. Together, then, you clean 1/10 + 1/11 of the house per hour:

 

1/10 + 1/11 = 11/110 + 10/110 = 21/110

 

Let x = the number of hours you clean together. Then (21/110)x represents the portion of the house you've cleaned together. You want to know how long it will take before 110/110 of the house is clean:

 

(21/100)x = 110/110

(21x)/100 = 1

21x = 100

x = 100/21

 

It will take you x = 100/21 = 4.76 hours to clean the house together.