Question 132054
Since Sam (or Stan?) can load the truck in 24 minutes, each minute he loads 1/24 of the truck.
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His brother's rate (call it B) is unknown. But if you multiply his rate by 15 minutes he
does B times 15 of the job. In that same 15 minutes Sam does 15*(1/24) of the job. So the equation
for their combined 15 minutes of work is:
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15/24 + B*15 = 1
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where 1 means the 1 job of loading the truck is done.
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The denominator 24 can be eliminated by multiplying the entire equation (all terms on both sides)
by 24 to convert the equation to:
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15 + (24*15)B = 24
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Get rid of the 15 on the left side by subtracting 15 from both sides to get:
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(24*15)B = 9
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On the left side multiply out the 24 * 15 to get 360 and the equation then is:
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360B = 9
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Solve for B by dividing both sides by 360 and you have:
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B = 9/360
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But you can divide both the numerator and the denominator by 9 to simplify the fraction to:
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B = 1/40
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This tells you that Sam's brother does 1/40 of the job per minute. So it will take him
40 minutes to do the entire 1 job by himself.
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Your "guess" was a good one. Hope this shows you a way in which the problem could be done.
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