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Math Help - Simultaneous linear equation

  1. #1
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    Question Simultaneous linear equation

    Hi,
    2 men and 7 children complete a certain piece of work in 4 days and 3 men and 5 children complete the same in only 3 days. Find the number of days required to complete the same work by 1 man or 1 child.
    When I solved these equations I got x=0.0909090 and y=0.54545454. but how to do further steps to calculate the number of days required to complete the same work by 1 man or 1 child?
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  2. #2
    MHF Contributor ebaines's Avatar
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    Re: Simultaneous linear equation

    I don't know how you have defined 'x' and 'y', but if they are the rates that 1 man or 1 child can work - expressed in terms of amount of job completed per day - then the time for one man or 1 child to complete the task alone is the inverse of that. However - by my calculations the rates of work by a man or a child are much less than what yuo have calculated. Please show us the two equations that you set up and solved. Remember to be consistent in terms of work completed = number of people times rate of work per person per day times days.
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  3. #3
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    Re: Simultaneous linear equation

    Quote Originally Posted by ebaines View Post
    I don't know how you have defined 'x' and 'y', but if they are the rates that 1 man or 1 child can work - expressed in terms of amount of job completed per day - then the time for one man or 1 child to complete the task alone is the inverse of that. However - by my calculations the rates of work by a man or a child are much less than what yuo have calculated. Please show us the two equations that you set up and solved. Remember to be consistent in terms of work completed = number of people times rate of work per person per day times days.
    Hello ebaines,
    I had modified the original problem to some extent. But it looks modification is not appropriate. So I am quoting original problem. Here it goes.:-
    2 men and 7children complete a certain piece of work in 4 days and 4 men and 4 children complete the same in only 3 days. Find the number of days required to complete the same work by 1 man or 1 child.
    answer:2x+7y=4
    4x+4y=3
    After solving these equations we get x=0.25 and y=0.5 Now what are the further steps to calculate the number of days required to complete the same work by 1 man or 1 child?
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  4. #4
    MHF Contributor ebaines's Avatar
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    Re: Simultaneous linear equation

    Unfortunately yuor equations are niot set uop correctly. What you have is "Number of men" times x plus numebr of children times y = time required to complete the job. But by that reasoning if you added more men or children it would take longer to complete the job, which is clearly not right. This is why I said to use: Work completed = number of people times rate per person times time. The rate here is job/(man-day) and job/(child-day). To complete 1 job the equations are:

    1 = (2x + 7y)4
    1 = (4x + 4y)3

    Once you solve for x and y you will have x = job/(man-day) and y = job(child-day); the inverse of those will give you (man-days)/job and (child-days)/job, respectively.
    Thanks from Vinod
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