Free Guide: Work/Rate Problems (Joint Work) in Psychotechnic and Dapar Tests

How to solve worker, faucet, and machine questions accurately, quickly, and without getting confused by fractions

Written by Eli Isaak • Phone: 054-5664932 • Ask me on WhatsApp

About Work/Rate Problems (Joint Work)

Work/rate problems deal with workers working together, faucets filling a pool, machines producing parts, and pipes draining a container. Such problems usually involve multiple entities, each finishing the work at a different time. Many examinees try to add times together and get a wrong answer, whereas in practice, there is one simple method that recurs in all these questions.

The key to success is to switch from "how long does it take?" to "how much work is done in one hour?" This amount is called the rate. Once we convert each entity into a rate, we can add rates (joint work), subtract rates (drainage or opposing work), and finally convert back to time. Below are 6 core methods for solving the most common types of questions on the test.

The Golden Triangle of Work/Rate Problems:

Work (W) = Rate (R) × Time (T)
When the entire work is "one task", it is denoted as 1, and then: Rate = 1 / Time (e.g., someone who finishes in six hours does 1/6 of the work per hour).
1
Calculating the Rate per Unit of Time
When a defined amount of output is given (parts, pages, liters), first calculate how much is done in one unit of time, and then use this rate to answer the question.
Example A: Quantity in a Given Time
A machine produces 90 parts in 3 hours. How many parts will the machine produce in 8 hours at the same pace?
  • Machine rate: 90 / 3 = 30 parts per hour
  • Work in 8 hours: 30 × 8 = 240
Answer: 240 parts
Example B: Time for a Given Quantity
A printer prints 450 pages in 15 minutes. How many minutes will it take to print 1,200 pages?
  • Printer rate: 450 / 15 = 30 pages per minute
  • Formula: T = W / R
  • Calculation: 1,200 / 30 = 40
Answer: 40 minutes
2
Joint Work (Adding Rates)
When several entities work together on the same task, their joint rate is the sum of their rates. The joint time is found by taking the reciprocal of the sum: if the joint rate is 1/5 per hour, the entire work will finish in 5 hours. The common mistake is to add or divide the times themselves.
Example A: Two Workers
Dana paints a room alone in 6 hours, and Ron paints the same room alone in 3 hours. In how many hours will they finish painting the room if they work together?
  • Dana's rate: 1/6 of the room per hour
  • Ron's rate: 1/3 of the room per hour
  • Joint rate: 1/6 + 2/6 = 3/6 = 1/2
  • Time: 1 / (1/2) = 2
Answer: 2 hours
Example B: Three Workers
Three workers can finish a job alone in 10 hours, 15 hours, and 30 hours. In how many hours will they finish it if they work together?
  • Sum of rates: 1/10 + 1/15 + 1/30
  • Common denominator 30: 3/30 + 2/30 + 1/30 = 6/30 = 1/5
  • Time: 1 / (1/5) = 5
Answer: 5 hours
3
Finding the Missing Worker's Time (Subtracting Rates)
When the joint time and the time of one of the workers are given, subtract the known worker's rate from the joint rate. What remains is the rate of the missing worker, which is then converted back to time.
Example A: One Known Worker
Noa and Yuval finish a project together in 4 hours. Noa alone finishes it in 12 hours. In how many hours will Yuval finish the project alone?
  • Joint rate: 1/4
  • Noa's rate: 1/12
  • Yuval's rate: 1/4 - 1/12 = 3/12 - 1/12 = 2/12 = 1/6
  • Yuval's time: 1 / (1/6) = 6
Answer: 6 hours
Example B: Two Faucets
Two faucets fill a pool together in 6 hours. The first faucet fills it alone in 10 hours. In how many hours will the second faucet fill the pool alone?
  • Joint rate: 1/6, first faucet rate: 1/10
  • Second faucet rate: 1/6 - 1/10 = 5/30 - 3/30 = 2/30 = 1/15
  • Time: 1 / (1/15) = 15
Answer: 15 hours
4
Filling and Draining (Opposing Rates)
When some entities are filling and others are draining (or when one worker undoes what another did), add the filling rates and subtract the draining rates. If the result is positive, the container will fill up; if negative, it will empty.
Example A: Faucet and Drain
A faucet fills an empty pool in 6 hours. A drain empties a full pool in 12 hours. In how many hours will the pool fill if both the faucet and the drain are open simultaneously?
  • Filling rate: +1/6
  • Draining rate: -1/12
  • Net rate: 2/12 - 1/12 = 1/12
  • Time: 1 / (1/12) = 12
Answer: 12 hours
Example B: Two Faucets and a Drain
An empty tank. Faucet A fills it in 4 hours, faucet B fills it in 12 hours, and a drain pipe empties it when full in 6 hours. In how many hours will the tank fill if all three are open together?
  • Filling rates: 1/4 + 1/12 = 3/12 + 1/12 = 4/12
  • Draining rate: 1/6 = 2/12
  • Net rate: 4/12 - 2/12 = 2/12 = 1/6
  • Time: 1 / (1/6) = 6
Answer: 6 hours

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