Learn how to solve problems on time required to complete a piece a work when a person A completes a piece of work in n days, then work done by A in one days = 1/n th part of the work.
Now we will apply the above concept for solving some real-life problems to find the time required to complete the allotted work.
Solved problems on time required to complete a piece a work:
1. Anthony and Billy can built a wall in 6 days, Billy and Corey can do it in 9 days and Corey and Anthony in 12 days.
In how many days will they:
(i) finish together?
(ii) finish separately?
Solution:
(Anthony + Billy)’S 1 day work = 1/6
(Billy + Corey)’s 1 day work = 1/9
(Corey + Anthony) ‘s 1 day work = 1/12
[(Anthony + Billy) + (Billy + Corey) + (Corey + Anthony]‘s 1 day work = 1/6 + 1/9 + 1/12
(2 Anthony + 2 Billy + 2 Corey)‘s 1 day’s work = 12 + 8 + 6/72
2(Anthony + Billy + Corey)’s 1 day’s work = 26/72
Therefore, (Anthony + Billy + Corey)’s 1 day’s work = 26/72 × 2
Therefore, together Anthony, Billy, and Corey can complete the work in 72/13 = 5.5 days.
Therefore, Anthony’s 1 day’s work = (Anthony + Billy + Corey)’s 1 day’s work – (Billy + Corey)’s 1 day’s work
= 13/72 – 1/9
= (13 – 8)/ 72
= 5/72
Therefore, Anthony finishes the work in 72/5 days.
Billy’s 1 day’s work = (Anthony + Billy + Corey)’s 1 day’s work – (Corey – Anthony)’s 1 day’s work = 13/72 – 1/12
= (13 – 6)/72
= 7/72
Therefore, Billy finishes the work in 72/7 days.
Corey’s 1 day’s work = (Anthony + Billy + Corey)’s 1 day’s work – (Anthony + Billy)’s 1 day’s work = 13/72 – 1/6
= (13 – 12)/72
= 1/72
Corey can finish the work in 72 days.
2. Daniel can do piece of work in 15 days and Josh can do it in 10 days. They work together in 3 days, then Daniel goes away. In how many days will Josh finish the remaining work?
Solution:
Daniel’s 1 day’s work = 1/15
Josh’s day’s work = 1/10
(Daniel + Josh)’s 1 day’s work = 1/15 + 1/10 = 2 + 3/30 = 5/30 = 1/6
(Daniel + Josh)’s 3 day’s work = 1/6 × 3 = 1/2
Remaining work = (1 – 1/2) = (2 – 1)/2 = 1/2 which is to be done by Josh.
We know that, 1/10 work is done by Josh in 1 day.
1 work is done by Josh in 1/1/10 day = 1/1 × 10/1 = 10 days
1/2 work is done by Josh in 10 × 1/2 days = 5 days
Therefore, Josh will finish the remaining work in 5 days.
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 Problems on Time required to Complete a Piece a Work 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.
Aug 10, 24 04:59 PM
Aug 10, 24 02:25 AM
Aug 10, 24 01:59 AM
Aug 10, 24 01:57 AM
Aug 06, 24 02:12 AM
Worksheet on Work Done in a Given Period of Time
Worksheet on Time Required to Complete a Piece of Work
Worksheet on Pipes and Water Tank
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.