How to solve the problem to work together

Objectives for the joint work familiar to students of many generations. They are often offered for final certification, however, the time to solve them in the school course of mathematics is given very little. Realizing the principle of the decision of tasks of such types, you are not confused in the exam.

You will need

• - collection of problems;
• - ability to solve systems of equations;
• - knowledge of methods of rational accounts.

Instruction

1. Determine what subtype the task is related to work together. Three main subtypes. This is the task to calculate time, speed of filling the pool via pipes with different bandwidth and on the calculation of the path traversed between two or more moving bodies. The last subtype is very similar to the task movement.
2. In General, the problem statement for the calculation of the time look like this. One worker can perform a task faster than the second. on the value of a. Together they will spend b hours. You'll find how much time will it take each to perform the entire scope of work. Take all the work for 1.
3. The time required for each, label as x and y. Find the productivity of each worker. To do this, 1 divided by the time, that is, x and y.
4. Express the equation as you do each for a while until they work together. To do this, multiply the capacity of 1/x and 1/y in a and add both numbers. The result - all the work, that is 1. Thus, the first equation you have will look like a(1/x + 1/y)=1.
5. The second equation of the system will represent the difference between x and y, which equals the number b. Solve system of equations by expressing one of the unknowns through the other. For example, y=b-x. Substituting this value into the first equation of the system, you can calculate x.
6. Problems of this type may differ from each other, but the principle remains the same. For example, you are given that a while two workers worked together, then one stopped working. The other has fulfilled the remaining job for some time. In any case, the entire amount will be equal to 1. In the same way as in the first case, indicate the time and the second one as x and y. Express performance by dividing the work on time.
7. Express, how much did each worker while they were working together, multiplying the productivity by the total time. Then run for the total time of the amount of work one Express through the volume of the second and make a system of equations.
8. Famous tasks in the pool are solved by the same algorithm, only for 1 you must take the entire volume of water. For the system of equations we first need to Express how much water flows or is poured from each tube per unit time. Then Express the amount of water from one pipe through another number and solve the system.