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Question 132054: Stan can load his truck in 24 minutes. If his brother helps him, it takes them 15 minutes to load the truck. How long does it take Sam's brother alone? Is the answer 40 minutes? I'm just taking a wild guess. If you could tell me the REAL answer and how you solved it, that would be awesome. Thanks.
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! 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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