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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
• 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
• 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. ;/
• 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.
• 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?
• 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. :)
• am sorry sal but i didn't understand a thing from .
• 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.
• 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)
• 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?
• 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
• this hurts my brain
• Ahhh my brain will burst from this question...!
It's really confusing.... :(