logo for solving-math-problems.com
leftimage for solving-math-problems.com

Work problem














































Andrei can build a wall in 6 days. Reagan had worked on the wall for three days alone before Andrei joined him. Together, they have completed the wall in three more days. How long will it take Reagan to build the wall alone?

Can you give me the solution regarding in this question. Thanks..

Comments for Work problem

Click here to add your own comments

Jan 17, 2010
work problem solution
by: Staff


1. You can look at the problem this way:

(work completed by Andrei) + (work completed by Reagan) = total work completed


2. Use fractions

(what fraction of the entire job was completed by Andrei) + (what fraction of the entire job was completed by Reagan) = 1 (that is, 1 completed job)


3. Before writing the equation, determine what fraction of the job each person can complete in 1 day


Andrei: since Andrei can complete the entire job (1 job) by himself in 6 days, the fraction of the job he can complete in 1 day = 1/6

Reagan: since the number of days Reagan will need to complete the entire job (1 job) by himself is unknown, that time can be represented by the variable “x”. Therefore, if Reagan can complete the entire job in “x” days, the fraction of the job he can complete in 1 day = 1/x


4. Write the equation


Andrei fraction + Reagan fraction = 1



(1/6 job per day)(only 3 days worked) + (1/x job per day)(entire 6 days worked) = 1


5. Solve the equation


(1/6)(3) + (1/x)(6) = 1

(3/6) + (6/x) = 1

(1/2) + (6/x) = 1

(1/2) – (1/2) + (6/x) = 1 – (1/2)

(6/x) = (1/2)

(6/x)(x) = (1/2)(x)

6 = x/2

(6)(2) = (x/2)(2)

12 = x

The Answer: Reagan can complete the entire job by himself in 12 days.



6. Since we now know that x = 12, check your answer using the original equation, shown at the beginning of step 5


(1/6)(3) + (1/12)(6) = 1

(3/6) + (6/12) = 1

(1/2) + (1/2) = 1

Staff
www.solving-math-problems.com

Jan 18, 2010
Thanks
by: joboy13

Nice and clear solution.. Many thanks..

Click here to add your own comments

Join in and write your own page! It's easy to do. How? Simply click here to return to Math Questions & Comments - 01.



Copyright © 2008-2015. All rights reserved. Solving-Math-Problems.com