DRT Formula - why and when do you subtract

falcios

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Sally and Lucy are running in the marathon. Sally runs at 7 mph and Lucy runs at 5 mph. If they start at the same time, how long will it be before they are 1/2 mile apart?

7x-5x=1/2

x=1/4 hour; 15 minutes

My question is why do you subtract 7x-5x and not add? My theory is that the miles apart is under 1 mph.

Also, is there a way to know when to add or subtract?

Thanks in advance.
 
Sally and Lucy are running in the marathon. Sally runs at 7 mph and Lucy runs at 5 mph. If they start at the same time, how long will it be before they are 1/2 mile apart?

7x-5x=1/2

x=1/4 hour; 15 minutes

My question is why do you subtract 7x-5x and not add? My theory is that the miles apart is under 1 mph.

Also, is there a way to know when to add or subtract?

Thanks in advance.

At time x hours, Sally is at location 7x miles from the start, and Lucy is at 5x.

To find how far apart two locations are, you subtract. Why would you add?
 
Sally and Lucy are running in the marathon. Sally runs at 7 mph and Lucy runs at 5 mph. If they start at the same time, how long will it be before they are 1/2 mile apart?

7x-5x=1/2

x=1/4 hour; 15 minutes

My question is why do you subtract 7x-5x and not add? My theory is that the miles apart is under 1 mph.

Also, is there a way to know when to add or subtract?

Thanks in advance.
Wow.

First, I like to think of the formula as \(\displaystyle r = \dfrac{d}{t}\). Why?

Because it is very easy to remember that a common way to measure speed is miles per hour (or kilometers per hour), which is a measure of distance divided by a measure of time. DRT as an acronym means nothing.

Furthermore \(\displaystyle r = \dfrac{d}{t} \implies d = r * t \implies t = \dfrac{d}{r}\)

so you only need to remember the rate formula: you can derive the distance and time formulas easily.

Two people leave the same spot at the same time going the same direction but at different rates, 5 and 7 miles per hour. They will go different distances. What is the difference in those distances? Hmm we call
a - b a DIFFERENCE. Is that a clue that maybe subtraction is appropriate?
 
You would add IF the question was along the lines of:
after how many hours will their combined distances travelled equal 84 miles?
84 / (7 + 5) = 7
 
You would add IF the question was along the lines of:
after how many hours will their combined distances travelled equal 84 miles?
84 / (7 + 5) = 7

Or if one of them ran in the wrong direction (which one hopes wouldn't happen in a marathon).
 
… DRT as an acronym means nothing …
I see instructors using the acronym as an adjective, when discussing distance-rate-time situations. For instance, they might write "DRT formulas", referring to the set of formulas in your post. :cool:
 
… My theory is that the miles apart is under 1 mph …
Your units are mismatched. You've written that a distance is less than 1 unit of speed.

Here's another way to think about the exercise (with no addition or subtraction).

Sally's running 2 mph faster than Lucy is. Therefore, the distance between them increases by 2 miles every hour they run. No matter how long they run, the distance between them increases proportionately to 2mph. Let's solve a proportion: "Two miles between them compares to one hour in the same way that half a mile between them compares to the unknown time we're looking for."

Let symbol t represent the solution, in hours. Write the proportion:

(2 mi) / (1 hr) = (1/2 mi) / (t hr)

The units are the same on each side, so they'll cancel.

To solve proportions, we rewrite the pattern A/B=C/D as A*D=B*C

Like this: (2)(t) = (1)(1/2)

2t = 1/2

t = 1/4
 
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I see instructors using the acronym as an adjective, when discussing distance-rate-time situations. For instance, they might write "DRT formulas", referring to the set of formulas in your post. :cool:
Well that at least makes a bit of sense, so thank you for educating me. But it does not materially help pull the information together in an easy way. It strikes me as something that seems helpful only to those who need no help. My experience as a tutor is that you must force yourself to remember what was confusing before you understood.
 
… [using lots of acronyms in beginning courses] does not materially help pull the information together in an easy way. It strikes me as something that seems helpful only to those who need no help …
I hear you. When I work with students face-to-face, I keep a running list in front of us, for defining stuff like symbols, abbreviations, "teacher's notation" -- as a reference for both of us! I also think it's better (as do you) to keep such abbreviations and extra names for things to a minimum, for beginning students. (Like teaching different formulas for 2step, 3step, and 4step equations, ugh.)
 
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