Question

Set up an equation and solve each of the following problems. (Objective 3)

Barry can do a certain job in 3 hours, whereas it takes Sanchez 5 hours to do the same job. How long would it take them to do the job working together?

Answer 1

Barry does the job in 3 hours. Therefore, Barry’s rate of doing work per hour is

...... (1)

Sanchez does the same job in 5 hours. Therefore, Sanchez’s rate of doing work per hour is

...... (2)

Let x represent the number of hours that Barry and Sanchez take to complete the job together. Therefore, their rate per hour when working to together is

...... (3)

Because the sum of individual rates must equal the rate of working together, we can write,

...... (4)

Here, r represents the rate per hour when Barry and Sanchez work together, is Barry’s rate per hour and is Sanchez’s rate per hour. Substitute (1), (2), (3) into (4) to get,

Multiply both sides by 15x to get,

Divide both sides by 8 to get,

Barry and Sanchez will take to complete the job together.