Andrew M. answered • 09/16/18

Tutor

New to Wyzant
Mathematics - Algebra a Specialty / F.I.T. Grad - B.S. w/Honors

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.