Word Problems/Proportions



When a proportion is used.  How does one know how to arrange the units?  For example,  If 3 men can rake a yard in 6 hours, how long will it take 6 men?

Is it 3 men/6 hours = 6 men/? hours

Is it 6/hours/3 men = ? hours/6 men


What determines how the units compare or correspond with what?

I thank you for your reply.

ANSWER: When we have men and hours, take that as m and h.

In the 1st equation, we have [3 m] / [6 h] = [6 m] / [x h].

Inverting both sides gives [6 h] / [3 m] = [x h] / [ 6 m].
{ Note that this is the 2nd equation }

Multiplying both sides by 6m cancels the m's and gives [36 h] / 3 = x h.

Since 36/3 = 12, we get 12 h = x h, so x = 12.

---------- FOLLOW-UP ----------


Can you double check you answer?  I think the answer is 3 men.

It would take 6 men half the time when working at the same rate.

I thank you for your reply.

I'm sorry about that.  That was a silly mistake on my part.
That reminds me of a test in math I took where I answered correctly on all the theory
but got points off for the arithmetic.

It appears you are trying to do a job in 6 hours.
They tell you it takes 3 men to do this.

If there are twice as many men, it would take half the time.
That means where there is a ? hours, it would be 3 hours.

I'm not sure where the answer "3 men" came from.

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Scott A Wilson


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