Combined work problems may look complex, but they are actually very simple once you memorize this basic equation.

For two operators that are working independently and at their own respective rates, x is the time it takes operator1 to do a certain job; y is the time it takes operator2 to perform the same job, and z is the time it takes both operators to do the job together.

How this equation is derived is outside the scope of this article. Suffice to say this equation will be necessary on every combined work problem you encounter – and it needs to be memorized. Inquisitive individuals can find how this equation is derived through a regular google search. Remember: a systematic approach to word problems is the key to solving them both quickly and accurately. A best practice approach is to use the work equation in conjunction with our standard word problem approach.

Example

Two machine types, Type R and Type S, operate at a constant rate. R does a job in 36 hours. S does same job in 18. If we use the same number of each type to do the job in 2 hours, how many Type R machines do we need?

1. 3
2. 4
3. 6
4. 9
5. 12

Solution

1. The question is asking how many type R machine are required
2. The problem statement already gives us the times for operator 1, 2 and combined to accomplish their jobs. The only unknown variable is the number of machines, so:

let x = # of type R machines

3. Write out the expression for the above statement incorporating our unknown variable



4. Solve for x.

The number of type R machines required is 6, so the answer is C.

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