2 of them can build a cabinet together in 12 hours. Rodney can build the cabinet alone in 16 hours. how long it will take Tomaso to build the cabinet alone?

Question

please help i really dont get this

Answer 1

Rodney can build a cabinet alone in 16 hours:

This means that Rodney builds 1/16 of a cabinet per hour

 

Together they build 1 cabinet in 12 hours.  If we call the

time it would take Tomaso to build a cabinet alone T, then

Tomaso does 1/T parts of a cabinet per hour

 

The sum of (1/16 + 1/T) is thus finished each hour.

 

This must sum to 1/12 since it takes 12 hours together to build a cabinet.

 

1/16 + 1/T = 1/12

Multiply through by Lowest Common Multiple of 12 and 16 ... 48

 

3 + 48/T = 4

 

48/T = 1

 

T = 48

 

Tomaso would take 48 hours to build a cabinet alone.