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Question 850678: A can do a certain work in the same time in which B and C together can do it. If A and B together could do it in 10 days and C alone in 50 days, then B alone could do it in....
Answer by josgarithmetic(39616)   (Show Source):
You can put this solution on YOUR website! Use all rates as Jobs per Days. Notice that C worker is given enough direct information for a rate value. Start with the rate for C, and create rate equations for B & C, and for A & B.
Rate for C:  jobs per day.
Let x = time for A to do 1 job.
Let y = time for B to do 1 job.
First sentence tells, rate for A is equal to the combined rate of B and C.
LCD is 50xy.
Second sentence tells, A and B together do the job in 10 days:
LCD is 10xy.
The system to solve for x and y is:
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Solving each of those for xy, and then equating each expression's formula for xy gives 
simplifying to
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Solving the linear equation for a variable, trying y,  ;
Picking either system equation, trying , and substitute the expression for y found,
Multiply left and right members by 2, and be sure to obtain this equation:
 -----do not try to divide either sides by x thinking that to be simplification; it's a common beginners mistake.
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The meaningful answer for x is that 
.. and use either system equation to find or solve for y. You can also use the linear  found earlier.
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