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### Course: Pre-algebra > Unit 14

Lesson 3: Comparing linear functions- Comparing linear functions: equation vs. graph
- Comparing linear functions: same rate of change
- Comparing linear functions: faster rate of change
- Compare linear functions
- Comparing linear functions word problem: climb
- Comparing linear functions word problem: walk
- Comparing linear functions word problem: work
- Comparing linear functions word problems

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# Comparing linear functions word problem: work

Sal is given a table of values that represents a person walking to work, and is asked to determine which verbal description represents someone starting at the same distance from work. Created by Sal Khan.

## Want to join the conversation?

- At3:25, shouldn't Sal NOT check the answer? Because I calculated the slope of Charles's chart, and it turned out to be -7/5. And the problem stated that Tammy and Charles did not go to work at the same speed, so since Charles's slope is -7/5, Tammy's slope shouldn't be -7/5, so therefore, the second choice shouldn't be the answer. Am I right? I am a bit confused by this.(7 votes)
- One strategy to learn with word problems is read carefully and reread multiple times.

The problem states: They walked at constants speeds, but not necessarily at the same speed. The phrase "not necessarily at the same speed" does not say they don't go at the same speed. It just means, they don't have to be going at the same speed. This means the speeds could be the same or different.

Hope this helps.(25 votes)

- I feel there is enough information given to determine that the only right answer would be she started at 900 meters and walked 7/5 m/s, the question IS what is possible however in 50 seconds she walked 70 meters, thus she HAD to be walking more then 1 m/s if she was walking equal to or less then 7/7 m/s (say 5/7 m/s) she would have been walking less then a meter a second and not more. So walking at 5/7 m/s she would not be able to walk 70 meters per 50 seconds.(8 votes)
- It doesn't imply "she walked 70 meters in 50 seconds", only Charles.(2 votes)

- ok i have a ligintiment question in the maths this

Mr. Mole and Bugs Bunny started digging their way into the ground from different locations at the same time. They each dug at a constant rate.

The following equation gives Mr. Mole's altitude (in meters relative to the ground) as a function of time (in minutes).

A=−4−0.6t

Bugs Bunny's altitude (in meters relative to the ground) as a function of time (in minutes) is given by the following table of values:

time (min) / altitude(meters)

2 / -1.6

9 / -7.2

16 / -12.8

Who dug faster?

A

Mr. Mole

B

Bugs Bunny

C

They both dug at the same rate

Who started at a higher altitude?

options the same

edit: what if one started on a hill and the other in the valley (this was my immediate thought) *why drag in bugs bunny *(6 votes) - Sometimes, I wonder if it's possible to use proportions instead of equations, graphs, or tables when solving relationship problems. Proportions seem like they could be a simpler and quicker method.(5 votes)
- Proportions only work when you can set up the equation as one fraction = another. Or, you have an equation like y=kx where "k" is the constant of proportionality. Anything different from those would not be a proportional relationshsip.(3 votes)

- If Charles is walking at 7/5 m/s and their speeds 'aren't necessarily the same' then how could Tammy be walking at 7/5 m/s too?(4 votes)
- It is not saying that they are walking at different speeds,it is only saying that they might be.(1 vote)

- if the slope is -7/5. There will be only one answer which is the second one right?

But what is confusing me is, what if -7/5 is the slope of charles but not tammy. So I think the answer can be anyone as long as she started 900 m from work.

Am I right?

Please answer me(3 votes)- Yes.We don't know Tammy's speed and we can't get that information from the table in the video,and they could be the same or different so you are right.(3 votes)

- This was made 5yrs ago trippin¯\
*(ツ)*/¯(3 votes) - but it says on a constant rate isn't it enough to determine that 5/7 is wrong?(3 votes)
- No because they could be walking at a constant rate of 5/7 meters per second.(0 votes)

- Would you always apply the same idea?(2 votes)
- What is the key in comparing a linear functions?(2 votes)

## Video transcript

Charles and Tammy live the
same distance from work, and they started walking
to work at the same time. They both walked
at constant speeds, though not necessarily
at the same speed. Charles' distance from work is
shown in the following table. So at 50 seconds, he's
830 meters from work. Then another 50 seconds
goes by, and now he's 760 meters from work. Another 50 seconds
goes by, and he's 690 meters from work,
which makes sense. He's getting closer and closer
to work as seconds pass by. He's walking to work. Which of these sentences
could possibly be true? Select all that apply. So what are these
sentences talking about? So it looks like they're
all talking about Tammy. Tammy started 830
meters from work and walked towards work
at 2 meters per second. She started 900 meters from
work and walked towards work at 7/5 meters per second. So all of these seem
to be statements about where did Tammy start
and how quickly did she walk to work? So let's think about which of
these could possibly be true. Well, the one thing
that we know is that they live the same
distance from work. So the distance
that Charles started walking from work, that's
the same distance that Tammy started walking from work. So let's figure out
what that distance is. So we see that every
50 seconds, so if we go from 50 to 100 seconds, so
if we add 50 seconds, or 50 seconds go by, it
looks like Charles traveled another-- let's see. To go from 830 to 760,
his distance from work decreased by 70 meters. And let's see if that
keeps holding up. It should because they're
moving at constant speeds. Another 50 seconds goes by,
and his distance from work decreases by another 70 meters. So what would have happened
50 seconds in the past? So what would
happen at 0 seconds? So 50 seconds before
he's at 830 meters, he would have been 70
meters further from work. So he would have been
900 meters from work, and we see that it's consistent. When 50 seconds pass by,
when we go from 0 seconds to 50 seconds, he goes from 900
meters away to 70 meters away. So once again, his distance
from work decreases by 70. Then another 50 seconds goes
by, it decreases by 70 again. Another 50 seconds, it
decreases by 70 again. So at time 0, Charles was
900 meters away from work. Now, we know that Tammy and
Charles live the same distance away from work. So Tammy would have also started
900 meters away from work. Now, they tell us that
they don't necessarily walk at the same speed. So we don't know what
Tammy's speed is. This hasn't in any way
constrained Tammy's speed. So we know that she
started 900 meters away. So we know that this
can't be the case. That says 830. We know that this
can't be the case. We know that this can't be
the case because they all talk about starting at a
distance other than 900 meters. And over here,
both of these, they say she started at
900 meters from work and walked towards work
at 7/5 meters per second. Well, that's possible. It's not necessarily true. They just haven't given us
information on her speed. But given the
information so far, this is definitely
a possibility. Likewise, Tammy
started 900 meters from work-- we
know that is true-- and walked towards work
at 5/7 meters per second. Well, once again,
that's a possibility. That hasn't been ruled
out by the information right over here. So these two are
both possibly true.