Calculate Work Done in a Given Time will help you to find how much work is finished in a given amount of time. If a person or group of members can complete the work in ‘y’ days, then the person or group of members can complete the work in one day is equal to \(\frac{1}{y}\). In this article, we are going to discuss the Work Done formula in a given time, calculation process, and sample problems along with explanations.

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## Work Done Formula

The basic formula for work done in a given time is equal to the product of time and rate of work. That is

Work Done (W) = Time(T) x Rate of Work (R).

The work done per day is called the rate of work. Work done is denoted by ‘W’, Time is denoted by ‘T’ and the rate of work is denoted by ‘R’. Work done is directly proportional to the Time and Rate of work. If the time taken by the person is increased, then the work done by the person will also increase.

### How to Calculate Work Done in a Given Time?

Follow the below steps to easily find out the solution for the given problems. They are

1. Note down the given information first (that is work done by one person)

2. Find the 1-day work by each person.

3. As per the equations, Calculate the total work done by all the members.

### Solved Examples on Calculating Work Done in a Given Time

Different types of Time and Work problems are available with the solution below. Follow the problems and learn the work done in a given time concept.

**Example 1.**

Andrew can complete the work in 10 days, Ria alone can complete the work in 20 days. Find in how many days the work is completed by working together?

**Solution:**

As per the given details, Andrew can take time to complete the work = x = 10 days.

Andrew can complete the work in one day = \(\frac{1}{x}\) = \(\frac{1}{10}\).

Ria can take time to complete the work = y = 20 days.

Ria can complete the work in one day = \(\frac{1}{y}\) = \(\frac{1}{20}\).

Andrew and Ria both can complete the work in one day = \(\frac{1}{x}\) + \(\frac{1}{y}\).

Substitute the values in the above equation. Then we will get \(\frac{x + y}{xy}\)

=\(\frac{1}{10}\)) + \(\frac{1}{20}\).

= \(\frac{2 + 1}{20}\).

= \(\frac{3}{20}\).

Andrew and Ria both can complete the total work = \(\frac{xy}{x+y}\).

= \(\frac{20}{3}\).

Therefore, the work is done by Andrew and Ria together in 6.67 days.

**Example 2.**

John can finish the work in 12 days and Mia can finish the same work in 15 days. John and Mia work together for 3 days after that Mia stops the work. So, In how many days Mia can complete the work?

**Solution:**

As per the given information, John can complete the work in 12 days. That is a = 12 days.

John can complete the work in one day = \(\frac{1}{a}\) = \(\frac{1}{12}\)th part of the work.

Mia can finish the work in 15 days. That is b = 15 days.

Mia can complete the work in one day = \(\frac{1}{b}\) = \(\frac{1}{15}\)th part of the work.

John and Mia working together for 3 days = \(\frac{1}{a}\) + \(\frac{1}{b}\).

Substitute the values in the above equation. Then we will get \(\frac{1}{12}\) + \(\frac{1}{15}\).

= \(\frac{5+4}{60}\).

= \(\frac{9}{60}\).

= \(\frac{9}{20}\).

Remaining work = 1- 9/20 = \(\frac{20 – 9}{20}\)= \(\frac{11}{20}\).

It is done by Mia.

As per the details, complete work is done by Mia in 15 days.

So, \(\frac{11}{20}\) of the work is done by Mia in 11/20× 15 = \(\frac{33}{4}\) days.

Therefore, Mia can complete the remaining work in \(\frac{33}{4}\)days.

**Example 3.**

A can do \(\frac{1}{4}\)th of the work in 20 days. B can complete the \(\frac{2}{5}\)th of the work in 15 days. If A and B are working together, in how many days the work will be completed?

**Solution:**

As per the given details, A Can finish the \(\frac{1}{4}\) of the work in 20 days.

So, A can complete the total work in 20 × 4/1= 80 days.

Therefore, A can do the work in 1 day = \(\frac{1}{80}\).

B can complete the \(\frac{2}{5}\) of the work in 15 days.

So, B can complete the total work in 15 × \(\frac{5}{2}\)= \(\frac{75}{2}\) days.

Therefore, B can do the work in 1 day = 2/75. (\(\frac{2}{75}\)).

A and B together can complete the work in one day = \(\frac{1}{80}\) + \(\frac{2}{75}\).

The L.C.M of 80 and 75 is 1200. So,

= \(\frac{15+16}{1200}\).

= \(\frac{31}{1200}\).

A and B can complete the total work = \(\frac{1200}{31}\).

Therefore, A and B can complete the total work in \(\frac{1200}{31}\) days.

**Example 4.**

William can make 1 toy in 10 hours and Warner can make 1 toy in 15 hours. If William and Warner working together, then how much time they will take to make 25 toys and also find the work done in 50 hours?

**Solution:**

As per the given information, William can make 1 toy in 10 hours.

So, Williams 1 hour work is equal to =\(\frac{1}{10}\).

Warner can make 1 toy in 15 hours.

So, Warner 1 hour work is equal to = \(\frac{1}{15}\).

If William and Warner working together, then the 1 hour work is equal to = \(\frac{1}{10}\) + \(\frac{1}{15}\).

\(\frac{3+2}{30}\).

\(\frac{5}{30}\).

\(\frac{1}{6}\).

So, By working with William and Warner together, 1 toy is prepared in 6 hours.

25 toys are prepared by working together = 25 × 6 = 150 hours.

William and Warner can prepare 1 toy in 6 hours.

If William and warner together work 50 hours, then they can prepare \(\frac{50}{6}\) toys. = \(\frac{25}{3}\) toys.

Therefore, William and Warner can make \(\frac{25}{3}\) toys in 50 hours.

**Example 5.**

David appoints three members to work on his site. They are A, B, and C, they can take 10 days, 20 days, and 30 days of time to complete the work. In how many days work is completed if they work together?

**Solution:**

As per the information, A can take 10 days of time to complete the work. That is a = 10 days.

A’s one day work is = \(\frac{1}{a}\) = \(\frac{1}{10}\).

B can take 20 days of time to complete the work. That is b = 20 days.

B’s one day work is = \(\frac{1}{b}\) = \(\frac{1}{20}\).

C can take 30 days of time to complete the work. That is c = 30 days.

C’s one day work is = \(\frac{1}{c}\) = \(\frac{1}{30}\).

If A, B, and C work together, then one day work is = \(\frac{1}{a}\) + \(\frac{1}{b}\) + \(\frac{1}{c}\).

= \(\frac{1}{10}\) + \(\frac{1}{20}\) + \(\frac{1}{30}\).

= \(\frac{6+3+2}{60}\).

= \(\frac{11}{60}\).

So, one day work by A, B, and C is equal to \(\frac{11}{60}\).

Total work is done by A, B, and C is \(\frac{60}{11}\).