Question 498927
If 2 boys can build 6 sandcastles in 3 and 1/3 hours, how long will it take for 3 boys to build 11 sandcastles? 
Thanks in advance!
<pre>
The easiest way to do job-worker-time problems is to use the formula:

{{{(W[1]T[1])/J[1]}}}{{{""=""}}}{{{(W[2]T[2])/J[2]}}}

where

W<sub>1</sub> = the number of workers in the first situation.
T<sub>1</sub> = the number of time units (hours in this case) in the first situation.
J<sub>1</sub> = the number of jobs in the first situation.

W<sub>2</sub> = the number of workers in the second situation.
T<sub>2</sub> = the number of time units (hours in this case) in the second situation.
J<sub>2</sub> = the number of jobs in the second situation.

W<sub>1</sub> = 2             W<sub>2</sub> = 3     
T<sub>1</sub> = {{{3&1/3}}}            T<sub>2</sub> = the unknown quantity 
J<sub>1</sub> = 6             J<sub>2</sub> = 11

{{{(W[1]T[1])/J[1]}}}{{{""=""}}}{{{(W[2]T[2])/J[2]}}}

Substituting:

{{{(2*3&1/3)/6}}}{{{""=""}}}{{{(3T[2])/11}}}

Multiply both sides by the LCD of 66 to clear of fractions:

{{{66((2*3&1/3)/6)}}}{{{""=""}}}{{{66((3T[2])/11)}}}

{{{11(2*3&1/3)}}}{{{""=""}}}{{{6(3T[2])}}}

Change {{{3&1/3}}} to {{{10/3}}}, Multtiply 6×3 on the right

{{{11(2*expr(10/3))}}}{{{""=""}}}{{{18T[2]}}}

Multiply both sides by 3

{{{3*11(2*expr(10/3))}}}{{{""=""}}}{{{3*18T[2]}}}

{{{cross(3)*11(2*expr(10/cross(3)))}}}{{{""=""}}}{{{54T[2]}}}

{{{11(2*10)}}}{{{""=""}}}{{{54T[2]}}}

{{{220 = 54T[2]}}}

{{{220/54 = T[2]}}}

{{{110/27 = T[2]}}}

{{{4&2/27 = T[2]}}}

Answer: {{{4&2/27}}} hours, or about 4 hours and 4.4 minutes.

Edwin</pre>