how to set this up? 3mph walking away; 6mph running back; 30 min total time; find d

HallsofIvy said:
Where others did everything in hours, JeffM used minutes. The "60" is "60 minutes per hour" so that "3 miles per hour" became "\(\displaystyle \frac{3}{60}= \frac{1}{20}\) miles per minute".


In Latex "\text" allows you to put actual text words in the math. "\dfrac" is almost identical to "\frac" showing a fraction.

"text": \(\displaystyle \text{This is an exponential function: }f(x)= e^x\)

"\frac": \(\displaystyle \frac{A}{B}\)

"\dfrac": \(\displaystyle \dfrac{A}{B}\)

Click on "Reply with Quote" to see the Latex code.
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Latex? First time I've heard of it. Is it available somewhere and would it be worth my while to learn it?
 
allegansveritatem said:
Yes, I get that but I don't understand why, when the equation presents both runner and walker, how to connect this d with the walker and thus answer the question. I can solve this problem in other ways than algebra, but I don't seem to be able to understand the algebra solution.
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What do you mean by "understand"? Algebra is intended to make abstract concepts more manageable. The fact that the concept remains abstract is irrelevant. Let the notation help you. Don't deny its usefulness.

You cannot solve this problem without algebra. Perhaps what you are doing as a solution is more internal and doesn't have nice notation, but that absolutely does not make it "other ... than algebra". If you do addition in your head, it's still algebra. Failure to write it down doesn't make it not algebra. From another perspective, calling it a algebra doesn't suddenly make it incomprehensible - or even different.

I know. There are plenty of voices telling students that mathematics is scary. Let's just ignore those voices.
 
tkhunny said:
What do you mean by "understand"? Algebra is intended to make abstract concepts more manageable. The fact that the concept remains abstract is irrelevant. Let the notation help you. Don't deny its usefulness.

You cannot solve this problem without algebra. Perhaps what you are doing as a solution is more internal and doesn't have nice notation, but that absolutely does not make it "other ... than algebra". If you do addition in your head, it's still algebra. Failure to write it down doesn't make it not algebra. From another perspective, calling it a algebra doesn't suddenly make it incomprehensible - or even different.

I know. There are plenty of voices telling students that mathematics is scary. Let's just ignore those voices.
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Here is what I meant by solving without algebra: the running took half as long to cover the same distance as the walking. Both walking and running took 30 mins. The walking, being half as fast, would have to take twice as long. How to divide 30 into two parts so that one part was twice as long as the other? Only one way: 20 mins and 10 mins. So...the walking took 20 mins and 20 mins at 3 miles an hour covers one mile, quod erat demonstrandum.
 
allegansveritatem said:
Here is what I meant by solving without algebra: the running took half as long to cover the same distance as the walking. Both walking and running took 30 mins. The walking, being half as fast, would have to take twice as long. How to divide 30 into two parts so that one part was twice as long as the other? Only one way: 20 mins and 10 mins. So...the walking took 20 mins and 20 mins at 3 miles an hour covers one mile, quod erat demonstrandum.
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Right. Logic and Algebra. Where is the "without" part?
 
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