# Work Formula

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‘Work’ in math involves math questions based on work done by certain number of people in a given amount of time period. In general when we observe, we know that work is dependent on the amount of time taken because to complete any task, a certain period of time is required. While solving questions related to work in math, we use this relation between work and time and calculate the total time taken to complete the given work accordingly.

Example 1: Matt takes 20minutes time to mow a lawn and Jake takes 30 minutes to mow the same lawn. How much time will it take if both Matt and Jake mow the lawn together?

Let time taken by Matt be, t1= 20mins
Let time taken by Jake be, t2= 30mins
Now time taken by both Matt and Jake to mow the lawn together be= t
Then the work formula==>1/t1+ 1/t2 = 1/t
Using the above formula, we get: 1/20+ 1/30= 1/t
==> (30+ 20)/ 600= 1/t==>50/600= 1/t

Hence we get: time, t= 600/50= 12minutes.

Example 2: Brett takes 3 hours to paint a house and Carl takes 5 hours to paint the same house. How much time will it take if both Brett and Carl paint the house together?

Let time taken by Brett be, t1= 3hours
Let time taken by Jake be, t2= 5hours
Time taken by both Brett and Carl to paint the house together be= t
Then the work formula==>1/t1+ 1/t2 = 1/t
Using the above formula, we get: 1/3+ 1/5= 1/t
==> (3+ 5)/15= 1/t==>8/15= 1/t

Hence we get: time, t= 15/8= 1.875hrs