Work Word Problem

Question

It takes Trevon 10 hours to clean an attic.  Cody can clean the same attic in 7 hours.  How long will it take them if they worked together?

Answer 1

Since Trevon takes 10 hours to clean the attic, he cleans 1/10 of the attic per hour. Since Cody take 7 hours to clean the attic, he cleans 1/7 of the attic per hour.

 

Together, that means they clean 1/10 + 1/7 of the attic per hour. That's an hourly rate of:

 

1/10 + 1/7 = 7/70 + 10/70 = 17/70

 

The portion of the attic they clean in x hours is (17/70)x. We'd like to know how long it will take them to clean 70/70 of the attic (all of it). So:

 

(17/70)x = 70/70

(17x)/70 = 70/70

17x = 70

x = 70/17

x ≈ 4.1176

 

Together, it will take them around 4.12 hours to clean the attic.