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You can put this solution on YOUR website!
if i understand this problem correctly.
\n" ); document.write( "sam is working on one machine.
\n" ); document.write( "bob is working on another machine.
\n" ); document.write( "i presume you are wanting to solve for x.
\n" ); document.write( "-----
\n" ); document.write( "rate * time = units produced
\n" ); document.write( "this would be the basic equation.
\n" ); document.write( "the number of units in this case is 1 machine for bob and 1 machine for sam.
\n" ); document.write( "-----
\n" ); document.write( "sam's rate is 1/x.
\n" ); document.write( "since rate * time = units produced, then
\n" ); document.write( "(1/x)*t = 1
\n" ); document.write( "dividing both sides of the equation by 1/x, we get:
\n" ); document.write( "t = 1/(1/x) = x
\n" ); document.write( "this means that sam takes x hours to complete 1 job.
\n" ); document.write( "-----
\n" ); document.write( "bob's rate is 1/(x+5)
\n" ); document.write( "since rate * time = units produce, then
\n" ); document.write( "(1/(x+5) * t = 1
\n" ); document.write( "dividing both sides of the equation by 1/(x+5), we get:
\n" ); document.write( "t = 1 / (1/(x+5) = x + 5
\n" ); document.write( "this means that bob takes x + 5 hours to complete 1 job.
\n" ); document.write( "-----
\n" ); document.write( "the problem states that both work for x hours.
\n" ); document.write( "this means that sam has finished his job since he only takes x hours to complete it.
\n" ); document.write( "this also means that bob, who is slower, still has 5 hours to go to finish his job.
\n" ); document.write( "sam, who is faster, only takes 3 hours to do what it takes bob 5 hours to do.
\n" ); document.write( "-----
\n" ); document.write( "what you have is a new job that takes 5 hours to complete at the rate of 1/(x+5), and that takes 3 hours to complete at a rate of 1/x.
\n" ); document.write( "-----
\n" ); document.write( "your equation is the same:
\n" ); document.write( "rate * time = units produced.
\n" ); document.write( "the units produced is still 1.
\n" ); document.write( "we have, however, a value for t.
\n" ); document.write( "-----
\n" ); document.write( "for bob to finish the job, the equation becomes:
\n" ); document.write( "rate = 1/(x+5)
\n" ); document.write( "time = 5
\n" ); document.write( "units produced = 1
\n" ); document.write( "r*t=u
\n" ); document.write( "(1/(x+5))*5=1
\n" ); document.write( "-----
\n" ); document.write( "for sam to finish the job, the equation becomes:
\n" ); document.write( "rate = 1/x
\n" ); document.write( "time = 3
\n" ); document.write( "units produced = 1
\n" ); document.write( "r*t=u
\n" ); document.write( "(1/x)*3 = 1
\n" ); document.write( "-----
\n" ); document.write( "since both of these equations = 1, then they are both = to each other.
\n" ); document.write( "so we have:
\n" ); document.write( "
\n" ); document.write( "this is the same as:
\n" ); document.write( "
\n" ); document.write( "if we multiply both sides of the equation by (x+5), we get:
\n" ); document.write( "
\n" ); document.write( "if we multiply both sides of the equation by x, we get:
\n" ); document.write( "
\n" ); document.write( "we can simplify this to be:
\n" ); document.write( "3*x + 15 = 5*x
\n" ); document.write( "15 = 2*x
\n" ); document.write( "x = 7.5
\n" ); document.write( "-----
\n" ); document.write( "if x = 7.5, then
\n" ); document.write( "x + 5 = 12.5
\n" ); document.write( "it takes sam 7.5 hours to do 1 job.
\n" ); document.write( "it takes bob 12.5 hours to do 1 job.
\n" ); document.write( "-----
\n" ); document.write( "sam's rate is 1/7.5 jobs per hour = .1333333..... jobs per hour.
\n" ); document.write( "bob's rate is 1/12.5 jobs per hour = .08 jobs per hour.
\n" ); document.write( "-----
\n" ); document.write( "to prove this is correct, we need to substitute in the original formulas.
\n" ); document.write( "the only formulas we have that we can use are:
\n" ); document.write( "bob takes 5 hours to complet a job that sam completes in 3 hours.
\n" ); document.write( "since rate * time = units
\n" ); document.write( "then
\n" ); document.write( "bob works 5 hours at a rate of (1/12.5) jobs per hour.
\n" ); document.write( "sam works 3 hours at a rate of (1/7.5) jobs per hour.
\n" ); document.write( "5 * (1/12.5) = .4
\n" ); document.write( "3 * (1/7.5) = .4
\n" ); document.write( "looks like they both did .4 of a job.
\n" ); document.write( "-----
\n" ); document.write( "this means that bob must have done .6 of his job when he quit.
\n" ); document.write( "let's see if that works out.
\n" ); document.write( "bob's rate is (1/12.5) jobs per hour.
\n" ); document.write( "he worked x hours.
\n" ); document.write( "x was found out to be 7.5
\n" ); document.write( "so 7.5 * (1/12.5) = .6
\n" ); document.write( "bob finished .6 of his job when he stopped working.
\n" ); document.write( "he would have taken 5 more hours to finish.
\n" ); document.write( "sam working on it instead and only took 3 hours.
\n" ); document.write( "-----
\n" ); document.write( "value of x is good.
\n" ); document.write( "equations prove out.
\n" ); document.write( "now all you need to do is understand what was done.
\n" ); document.write( "hopefully this helped.
\n" ); document.write( "-----
\n" ); document.write( "the key was rate times time = units produced.
\n" ); document.write( "units produced was 1 for each of them.
\n" ); document.write( "their respective rates were given:
\n" ); document.write( "1/x for sam
\n" ); document.write( "1/(x+5) for bob.
\n" ); document.write( "the key to solving the problem was the job that was left to finish.
\n" ); document.write( "we didn't know what proportion of bob's job was left, but we did know that we could look at the remaining portion as 1 job.
\n" ); document.write( "we discovered what proportion was left after we solved for x.
\n" ); document.write( "-----
\n" ); document.write( "any questions email to gonzo@gmx.us and i'll try to help you understand better if you are still confused.
\n" ); document.write( "-----
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