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Thread: Applications of Linear Equations, Equations and Inequalities, Shared Work

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    Applications of Linear Equations, Equations and Inequalities, Shared Work

    Please help me solve the following problem, the answer manual states 18 minutes, but I cannot figure out how.

    John & Eric work at Firestone, John can install a set of tires in 45 minutes, and Eric can install a set in 30 minutes. If they work together how long will it take them?

    When responding please show every step in the solution.

    Retro
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    Re: Applications of Linear Equations, Equations and Inequalities, Shared Work

    We help....don't do homework...

    Hint: in 1 minute, 1/45 + 1/30 = 1/18 of job gets done.
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    Re: Applications of Linear Equations, Equations and Inequalities, Shared Work

    Quote Originally Posted by retro View Post
    When responding please show every step in the solution.
    Retro
    Hi Retro, that sounds like a command. Are you asking for help or are you telling us what to do? I will tell you once again: we will help you when you show us your work and tell us what about your work you do not understand.
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    Re: Applications of Linear Equations, Equations and Inequalities, Shared Work

    Quote Originally Posted by retro View Post
    Please help me solve the following problem....When responding please show every step in the solution.

    Retro
    You probably don't realize it but these two comments are contrary. We can help you do the work but you will ultimately have to understand how to do the work yourself at some point.

    So tell us what you think can be done to solve the problem. We'll point out if/when you go wrong and give some advice on how to do the rest.

    -Dan
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    Re: Applications of Linear Equations, Equations and Inequalities, Shared Work

    When two people work together, their rates add.

    "John can install a set of tires in 45 minutes" so what is John's rate of work in "set of tires per minute"?

    "Eric can install a set in 30 minutes" so what is Eric's rate of work?
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    Re: Applications of Linear Equations, Equations and Inequalities, Shared Work

    The way I would work this is to find:

    $\displaystyle \text{lcm}(30,45)=90$

    So, I would look at the number of tasks each can do in 90 minutes, compute the total sum, and then divide 90 minutes by this total to find the time required for both working together to complete one task.
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    Re: Applications of Linear Equations, Equations and Inequalities, Shared Work

    Quote Originally Posted by retro View Post
    John can install a set of tires in 45 minutes,
    and Eric can install a set in 30 minutes.
    If they work together how long will it take them?
    Same as ye olde speed = distance/time problems;
    j = John's speed in mph, e = Eric's speed in mph;
    distance travelled (the "job") = 1 mile

    John:@j................1...............>3/4 hr.
    Eric:@e.................1...............>1/2 hr.
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    Re: Applications of Linear Equations, Equations and Inequalities, Shared Work

    Thank you, I was able to figure with your hint
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    Re: Applications of Linear Equations, Equations and Inequalities, Shared Work

    Okay, since I hate to leave things hanging, here is the solution:
    "John can install a set of tires in 45 minutes" so John's rate of work is 1/45 "set of tires per minute".
    "Eric can install a set in 30 minutes" so Eric's rate of work is 1/30 "set of tires per minute".

    Working together, their rates add: 1/45+ 1/30= 2/90+ 3/90= 5/90. Together they take 90/5= 18 "minutes per set of tires".
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    Re: Applications of Linear Equations, Equations and Inequalities, Shared Work

    John can install 4 tires in 45 minutes. That is 11.25 minutes per tire.

    Eric can install four tires in 30 minutes. That is 7.5 minutes per tire. If they each do two tires, that will be 22.5 minutes (Eric will finish 7.5 minutes early, and while he could try to help, he would probably just get in the way). If John does one while Eric does 3, that is also 22.5 minutes for all four tires (again, John could try to help with Eric's third tire, but would probably get in the way).
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    Re: Applications of Linear Equations, Equations and Inequalities, Shared Work

    Quote Originally Posted by DenisB View Post
    Hint: in 1 minute, 1/45 + 1/30 = 1/18 of job gets done.
    So 1/(1/18) = 18 minutes ; mine's better than all of yours
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    Re: Applications of Linear Equations, Equations and Inequalities, Shared Work

    Quote Originally Posted by DenisB View Post
    So 1/(1/18) = 18 minutes ; mine's better than all of yours
    You all assume the job is continuous. In the solution I gave, it is discrete. Only one person can put a tire on a car at a time. I think my answer is better. ;-)
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