# how to solve work done problems

We’ll learn in this post that how to solve work done problems and that how long it takes one person to complete a piece of work in 10 hours and another person in 12 hours, and how long it takes them to accomplish the same job while they’re working together, and so on. These questions can also be answered using the following simple procedure.

## Definition of Rate of Work

Rate of working of any person is work done divided by time taken.

## Formula For Rate of Work

Rate = Work Done/Time Taken

## Examples to Solve Work Done Problems

1) rock’s rate = 50/1 words per minute = 50 words per minute if he types 50 words in one minute.

2) John’s rate = 4/2 burgers per day = 2 burgers per day if he eats 4 burgers in 2 days.

3) Take work done = 1, if work is not clearly indicated. For example, if Adnan finishes a job in 6 days, his rate of work will be 1/6 (we’ve just assumed work = 1).

**Remember:** When two or more people work together, their total rate of work equals the sum (+) of their individual rates.

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## Solve Problems on Rate of Work Done

**Problem 1:** Trump finishes a task in three hours. In 5 hours, Bush completes the same task. How long will it take them to finish the job together?

**Solution:**

**Step 1:** Rate of Trump = A = work done/ time taken = 1/3

**Step 2:** Rate of Bush = B = work done/ time taken = 1/5

**Step 3:** When Trump & Bush work together, their rates will be added, so,

combined rate = A + B = 1/3 + 1/5 = 8/5

**Step 4:** The final part of the problem is to find the time taken by again using the same formula:

Time Taken = 1 ÷ 8/15 = 15/8 hours

Convert this value into minutes by using 1 hour = 60 minutes,

So our final answer is: Time Taken = 15/8 x 60 minutes =15/2 x 15 minutes = 225/2 minutes = **112.5 minutes (ANSWER).**

**Hints on Problem 1:**

1) Because work is not stated, work done has been set to 1 in all three circumstances.

2) In the question, you were asked to calculate the amount of time it takes for Trump and Bush to work together. As a result, the fourth and last stage is critical. Your answer will be incorrect if you find the combined rate by adding the two rates and merely say the final answer is 8/15 hours without mentioning the last step (which is actually the rate of two people and NOT the time taken).

**Problem 2:** If A can write 100 words in six minutes and A and B can do the same task in four minutes. When working alone, how long will B take to do this task?

**Solution:**

**Step 1:** Rate of A= work done/ time taken = 100/6 = 50/3

**Step 2:** When A & B work together, their rates will be added, so,

combined rate = A + B =

Rate of A+B = Work Done/ Time Taken when working together

Rate of A+B = 100/4 = 25

(Here put value of A = 50/3 & B= 25)

So, A+B = 50/3 + B = 25

B = 25 – 50/3 = 25/3

**Step 3:** The final part of the problem is to find the time taken by B again using the same formula:

Time Taken = 1 00 ÷ 25/3 = **12 minutes. (Answer).**

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