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## SAT (Fall 2023)

### Course: SAT (Fall 2023) > Unit 10

Lesson 1: Heart of algebra- Solving linear equations and linear inequalities — Basic example
- Solving linear equations and linear inequalities — Harder example
- Interpreting linear functions — Basic example
- Interpreting linear functions — Harder example
- Linear equation word problems — Basic example
- Linear equation word problems — Harder example
- Linear inequality word problems — Basic example
- Linear inequality word problems — Harder example
- Graphing linear equations — Basic example
- Graphing linear equations — Harder example
- Linear function word problems — Basic example
- Linear function word problems — Harder example
- Systems of linear inequalities word problems — Basic example
- Systems of linear inequalities word problems — Harder example
- Solving systems of linear equations — Basic example
- Solving systems of linear equations — Harder example
- Systems of linear equations word problems — Basic example
- Systems of linear equations word problems — Harder example

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# Linear function word problems — Harder example

Watch Sal work through a harder Linear functions word problem.

## Want to join the conversation?

- I am really confused on what this question is asking(30 votes)
- The question is asking how close Minli is to her house. She starts at her school, which you know is 1.4mi from her house. Her distance from home then would be 1.4mi minus how much she's walked. To find how much she's walked, you first need to find the rate of her walking. She normally walks the 1.4 mi in 24 minutes, which means she's walking at a rate of 7mi every 120 minutes. As she's getting closer to her house, time is passing, so the answer is d = 1.4 - 7t/120(57 votes)

- I would never be able to this by myself because how would i know that i need to multiply the 1.4/24 by 10? is this something yu just think about? why 10, why not 100, 20 or 55? i'd have just tried to solve it in the same form. it just wouldn't occur to me. ;/(24 votes)
- That step was not necessary, he did it to make this question easier. If you find that that kind of thing makes the question harder, you can just not do it. He multiplied the top and bottom by 10 to change 1.4 to 14 since whole numbers are easier than decimals. You could multiply by 100 and get 140/2,400 if you wanted. 10 is just that first number that comes to my mind (and presumably Sal's too) since multiplying by 10 moves the decimal left one place, changing 1.4 to 14.(28 votes)

- Why is the distance from school and home not the same? If the home is 1.4 miles away from the school, why is the distance from school to home any different?(20 votes)
- There is something to be taken in account. A notable point is that with the distance from school to her house ,1.4 m. they have also provided us the time which is 24 minutes. But in the case of from house to her school we don't know the time plus we are not provided the distance because this is linear inequality and if they would have done that, the word problem would be something else which will not be a linear inequality. What if she goes to the through bus or car? The time will surely decrease so will the distance as change in rate.

Hope it will help! Good luck learning SAT. :)(15 votes)

- am sorry sal but i didn't understand a thing from1:30.(6 votes)
- This question is all about distance, rate (speed) and time, which is pretty familiar. d =rt

The reason this is called a "harder" problem is you have to answer by figuring out which function matches the situation described, which is`distance remaining`

instead of distance traveled, which would be simpler. It might help you to draw a diagram. Remember that this student is starting at school and walking toward home. If she goes all the way home, she travels 1.4 miles. She knows from doing this a jillion times that it takes about 24 minutes, so the rate she travels is 1.4/24, which is 14/240, which simplifies to 7/120 of a mile per minute traveled. So, for every minute she travels, that total distance she has to walk is reduced by 7/120 of a mile. The rate = d/t (speed)

Now to build the function (equation)

In this problem, we have`distance from home`

=`total distance to travel`

-`distance already traveled`

.

The equation we have to write looks a little like the equation for a line, only instead of

y = mx + b, we have y = b + mx, and we have to subtract, because the more minutes she walks, the less distance she still has to travel.

Here we have**distance from home**=**total distance to travel**-`distance already traveled`

.

d = 1.4 -`distance already traveled`

.

The`distance already traveled`

is the rate we have figured out times the number of minutes she has walked (t), and that was`7/120 t`

So, that gives us an answer of

d = 1.4 -`7/120 t`

All the other options mix up the parts of the equations so they don't represent this trip from school to home.(28 votes)

- I don't understand why you subtracted distance from school from 1.4, why not add it? The distance should be constant. The distance from school to home should be constant i.e(1.4)(6 votes)
- how is distance between home and school not the same??

somebody answered in the comments below that what if she takes the bus back to home but it is CLEARLY mentioned that she walks back to school and even if she takes the bus or car or whatever how come distance changed?

suppose my school is at a distance of 10m from my home then how come my home would not be at a distance of 10m from my school?(5 votes)- do not get confused here in the question it says minli already walked a distance d in time t so now she is not in school she is walking towards he home. that is why distance is different(3 votes)

- this hurts my brain(6 votes)
- Ahhh my brain will burst from this question...!

It's really confusing.... :((5 votes) - If it is 1.4 miles to go from school to her house, wouldn't it be the same going back?? I don't understand where she is going. Why would we be subtracting 1.4 miles? and where is the other distance coming from?(4 votes)
- There is something to be taken in account. A notable point is that with the distance from school to her house ,1.4 m. they have also provided us the time which is 24 minutes. But in the case of from house to her school we don't know the time plus we are not provided the distance because this is linear inequality and if they would have done that, the word problem would be something else which will not be a linear inequality. What if she goes to the through bus or car? The time will surely decrease so will the distance as change in rate.

Hope it will help! Good luck learning SAT. :)(2 votes)

- At part 1.34 i just get confused.(3 votes)

## Video transcript

- [Narrator] Minli's house is located 1.4 miles from her school. When she walks home from school, it takes her an average of 24 minutes. Assuming that Minli
walks at a constant rate, constant rate, we can figure that out, because we know how far she walks in a certain amount of time. Which of the following
functions best models Minli's distance from home, D, in miles. So we want distance in miles. If she has walked a total of T minutes. So T is going to be in minutes, so all our units are gonna
be minutes and miles, and that's good because
they gave us things in terms of minutes and miles. If this was in seconds or hours, we would have to do some conversion. So let's just think about her rate, her constant rate, that
they're talking about. The rate that Minli walks. Well she covers 1.4 miles, she covers 1.4 miles, in 24 minutes, 24 minutes. Well this isn't a pretty fraction with the decimal in the numerator so let's multiply the numerator
and the denominator by 10 so that we get rid of this decimal. So that's going to be equal to
14 over 240 miles per minute. And then we can further simplify that. The numerator and the denominator
are both divisible by two, so this is going to be, let's see, 14 divided by two is seven. 240 divided by two, over
120, miles per minute. Miles per minute. So we were able to figure
out Minli's constant rate. Now we need to figure out D. We need to figure out D. We have to be very careful. D is Minli's distance
from home, from home. She's leaving from school and
it's her distance from home. Remember her home is 1.4
miles from her school. So there's a bunch of ways
that we can tackle it, but maybe the easiest one is, well, what's her distance if you wanted to say distance from school. Distance from school. Distance from school. That's just going to be her rate times T, times how much time has passed by. As when time is zero, she's
going to be at her school. As time increases in
minutes, she's going to get further and further away from her school. But her distance from home, her distance from home,
is going to be 1.4 miles minus the distance from school. So, let me just write D, 'cause this is what we care about, D, which is her distance,
in miles, from home. Distance in miles from home. That's going to be 1.4,
minus distance from school. Minus distance from school. And if that doesn't make
sense, just think about it. If this is her home right over here, I'll write H for home. If this is her school
right here, S for school, we know that this distance
right over here is 1.4 miles. Now she has walked... If she has walked, say... I don't know, let me do
this in another color. If she has walked .4 miles, if this is 0.4 miles right over here, then her distance from home is gonna be 1.4 miles minus that. It's going to be, it's going to be this
distance right over here. So distance from home is going to be 1.4 minus the distance from school. And what's that going to be? Well that's just going to be 1.4 minus the rate times the time. What's the rate? Seven 120ths miles per minute. We got the units right, and so this is D, is going to be equal to
1.4 minus seven over 120 T. And if we look at the choices, well that's going to be
this first choice over here. And it's fun to look at the other choices and to think about well how could we have ruled them out fairly quickly? Well this one has 1.4, the distances between the
two places, minus 24T. Well this isn't the rate right over here, that's how long it takes her
to walk, it's not the rate, so you can rule that one out. This one is 1.4 minus the
reciprocal of the rate, so that's a strange answer. And this one, this one makes it look like she's getting further
and further from home as time gets bigger. Notice this one right over here, it does correctly say at time zero she's going to be 1.4 miles from her home, which is accurate because at time zero she's going to be at her school. But then after one
minute, after two minutes, after three minutes, she's going to get, based on this model, further
and further away from her home. So this would be a case where she's walking away from home from her school, so you would rule that one out as well.