Setting up the verbal model.

Question

Working alone Suzy can clean the fourth floor of Euclid Towers in 3 hours. Ralf can clean the fourth floor of Euclid towers in 5 hours by himself. How long will it take Suzy and Ralf to clean the fourth floor of Euclid towers if they work together?

Answer 1

There are several ways to set up the equation.

I do it like this.

 

let x = number of hours they work together.

the part of the total job Suzy completes in x hours is x/3

the part of the total job Ralf completes in x hours is x/5

the total job = 1

 

therefore x/3 + x/5 = 1

 

5x/15 + 3x/15 = 1

 

8x/15 = 1

 

x = 15/8 hours = 1 7/8 hours

 

Suzy completes 5/8

Ralf completes 3/8

and the sum of the fractions is 1.