To calculate work done in a given time in general if a person A completes a piece of work in a ‘n’ days, then A’s one day work = 1/n.
If a man takes 10 days to complete a piece of work, then according to the unitary method work done in one day = 1/10.
Now we will apply the concept of solving some real-life problems to find the work done in a given period of time.
Solved examples to calculate work done in a given time:
1. Adam can do a piece of work in 15 days and Brandon can finish it in 10 days. They work together for 5 days and then Adam goes away. In how many days will Brandon finish the remaining work?
Solution:
Adam can finish the work in 15 days.
Therefore, Adam’s 1 day’s work = 1/15
Brandon can finish the work in 10 days.
Therefore, Brandon’s 1 day’s work = 1/10
So, (Adam + Brandon)‘s 1 day’s work = 1/15 + 1/10 = (2 + 3)/30 = 5/30 = 1/6
Therefore, (Adam + Brandon)‘s 5 day’s work = 5 × 1/6 = 5/6
Remaining work = 1 – 5/6 = 6-5/6 = 1/6
This remaining work has to be done by Brandon.
Complete work is done by Brandon in 10 days.
Therefore, 1/6 of the work is done by Brandon in (10 × 1/6) days = 5/3 days.
Hence, the remaining work is done by Brandon in 5/3 days.
2. Alex can do 3/4 of the work in 12 days and Ben can do 1/8 th of the work in 2 days. In how many days both Alex and Ben can together do the work?
Solution:
3/4 of the work is done by Alex is 12 days.
Therefore, the whole work will be done Alex in 12 × 4/3days = 16 days.
Therefore, Alex’s day’s work = 1/16
Similarly, 1/8 of the work is done by Ben in 2 days.
Therefore, the whole work will be done Ben in 2 × 8/1 = 16 days
So, Ben’s 1 day work = 1/16
Now (Alex + Ben)’s 1 day’s work = 1/16 + 1/16 = 2/16 = 1/8
Therefore, (Alex + Ben) together will complete the work in 8 days.
More problems to calculate work done in a given time:
3. Nancy can embroider a dress in 15 hours while Sam can do the same in 10 hours. Working together how much time will they take to embroider 5 dresses?
How many dresses will be embroidered in 54 hours?
Solution:
Nancy can embroider a dress in 15 hours.
So, Nancy’s 1 hour work = 1/15
Also, Sam can embroider a dress in 10 hours.
So, Sam’s 1 hour work 1/10
Nancy’s and Sam’s 1 hour work = 1/15 + 1/10 = 2+3/30 = 5/30 = 1/6
So, they will together take 6 hours to embroider 1 dress.
So, working together, time taken to embroider 1 dress = 6 hours.
Therefore, time taken to embroider 5 dresses = (6 × 5) hours = 30 hours.
Also, number of dresses embroidered in 6 hour = 1
Number of dresses embroidered in 1 hour = 1/6
Therefore, number of dresses embroidered in 54 hours = 1/6 × 54 = 9
Calculate Time to Complete a Work
Calculate Work Done in a Given Time
Problems on Time required to Complete a Piece a Work
Problems on Work Done in a Given Period of Time
Problems on Pipes and Water Tank
7th Grade Math Problems
From Calculate Work Done in a Given Time to HOME PAGE
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.
Sep 17, 24 02:25 AM
Sep 17, 24 01:47 AM
Sep 17, 24 12:10 AM
Sep 16, 24 11:24 PM
Sep 16, 24 02:40 PM
Worksheet on Work Done in a Given Period of Time
New! Comments
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.