cam & Lj clean house in 2 hours when working together. kate takes 4 hours alone. when working all 3 together how long will it take to clean house?

Question

I want to know how to make up an equation and then the process to solve it. I am stuck and my alg. 2 teacher's explaining is confusing.

Answer 1

Let x = time it takes if all three work together

 

Portion done by Cam and LJ in i hour = 1/2

Portion done by Kate in 1 hour = 1/4

Portion done by all of them in 1 hour = 1/x

 

So, 1/2 + 1/4 = 1/x

 

Multiply through by the LCD, 4x:

 

2x + x = 4

 

3x = 4

 

 x = 4/3 hrs

 

 

Answer 2

rate of cam and lj = 1 house/2 hr so they clean at a rate of 1/2 house/hr

kate = 1 house/ 4 hr so 1/4 house/hr

 

1/2 house/hr + 1/4 house/hr = 3/4 house/hr which translates to 1 house per  4/3 hour = 1 1/3 hour = 1 hour 20 minutes.