x/2 + x/4= 1

Question

Cecil can clean the yard in 2hrs by himself. Darren can clean the yard in 4hrs. If they work together how long will it take them to clean the yard together?

Answer 1

If Cecil can clean the yard alone in 2 hours, then he can clean 1/2 of the yard in 1 hour

If Darren can clean the yard alone in 4 hours, then he can clean 1/4 of the yard in 1 hour.

Let x = the amount of time that the two of them can clean the yard working together.

Then, the two of them can clean 1/x of the yard in 1 hour. 

 

We now set up the following equation:

 

1/2 + 1/4 = 1/x

 

Multiply both sides of this equation by the LCD, which is 4x.

 

2x + x = 4

3x = 4

x = 4/3

 

Together, two can clean the yard in 4/3 = 1 1/3 hours = 1 hour and 20 minutes