Question 315892
Let's first find the hourly rate of each group:
If X+Y can do the job in 4 hours, then they can do {{{1/4}}} of the job in 1 hour.
If X+Z can do the job in 6 hours, then they can do {{{1/6}}} of the job in 1 hour.
If X+Y+Z can do the job in 3 hours, then they can do {{{1/3}}} of the job in 1 hour.
These can be expressed as:
1) {{{X+Y = 1/4}}}
2) {{{X+Z = 1/6}}}
3) {{{X+Y+Z = 1/3}}}
Express the first 2 equations in terms of X.
1a) {{{Y = (1/4)-X}}}
2a) {{{Z = (1/6)-x}}} Now substitute these for Y and Z in equation 3) to get:
3a) {{{X+((1/4)-X)+((1/6)-X) = 1/3}}} Simplify and solve for X.
{{{X = 1/12}}}
To find the hourly rate of Y, subtract {{{X = 1/12}}} from equation 1).
{{{X+Y = 1/4}}}-{{{X = 1/12}}} 
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{{{Y = 1/6}}} This is the hourly rate of Y, so it will take Y 6 hours to complete the job.