Lori can clean the garage in 3 hours, but it takes Steve 4 hours to do the same job. How long will it take them to clean the garage if they worked together?

Question

Lori can clean the garage in 3 hours, but it takes Steve 4 hours to do the same job. How long will it take them to clean the garage if they worked together?

 

Need to solve with d=r*t

 

Answer 1

Let x be the rate at which Lori works (how many garages she can clean alone in 1 hour), and let y be Steve's rate (same idea).

 

Since Lori can clean the garage in 3 hours, her rate is x = 1/3 (one garage cleaned in 3 hours). Also, Steve's rate would be y = 1/4, by the same reasoning.

 

Their rate working together is x + y, so

 

1/3 + 1/4 = 7/12.

 

This means they can clean 7/12 of the garage in one hour, so the time it would take them to clean it completely is 12/7. This is because the amount of work done is 1 divided by the rate at which it is completed.

 

12/7 = 1 5/7 hours.

 

Notice that this is a reasonable answer since the time it would take them together would be LESS than the time it would take each separately. (Unless, of course, they do not like working together.)