Word Problems Uniform Motion

# Word Problems Uniform Motion

>>Hi, uniform motion problems
are my favorite word problems. Alright so let’s start
with a little story. It’s 12:00 pm. Super Snail and Sergeant
Salt, that’s Super Snail, that’s Sergeant Salt,
they’re 12 inches apart and they start traveling
towards each other. Super Snail travels at
4 inches per minute. Sergeant Salt travels
at 2 inches per minute. So they’re not very fast. Ok so here comes Super
Snail and it’s 1, 2, 3, 4. That took him a minute
to get to here. And Sergeant Salt, he
does 2 inches per minute so 1, 2, that’s a minute. So after 1 minute
that would be here and here, still not together. So we don’t want to sit
here and wait and find out how long it’s going
to take for them to meet so we make a little problem. So we know that Super
Snail’s distance is made by the formula rate times time,
same with Salt, rate times time. We know that his rate is 4. We don’t know how long
he’s been traveling. Salt is 2, same thing,
t. And what we have to find now is now
what’s the relationship between these two distances? So if you follow their distance, that right there is the total
distance traveled by the salt. And that is the total
distance travelled by the snail, right in here. That’s d for the snail. That’s d for the salt. Ok? And how far apart
are they, 12 inches. So together they have
to travel 12 inches. If we have the situation where they’re traveling
towards each other, there’s a total distance
that’s given and their distances both
have to add up to 12. So if we take the 4t and the 2t, we add them up, we
have to get 12. And that gives us 2 minutes. So after 2 minutes
they would meet. Let’s see if it’s true. So this one does 4 inches
every minute so that’s 1 minute and then 1, 2, 3, 4 and 1, 2 so that’s when they
would meet right there. And it’s true, 2
minutes, 1, 2, 1, 2. So in each problem we’re going
to have two different items, two objects and they’re going to
be traveling towards each other, away from each other or
in the same direction. So what we have to do is find
the distance formula for each and then find the relationship between those distances,
that’s it. And there’s going
to be a nice pattern so let’s try another one. So read the problem to yourself
and then see if you can figure out what goes in where. So this is Sally, that’s
why I have ds there. This is Jimmy. Ok, ok, so Sally’s rate is 1
foot per second, Jimmy’s is 2. And the problems asking
when Jimmy starts the race? That means we have the t for
Jimmy so that’s t for Jimmy. And all you have to
do is ask yourself now for Sally did she have
more or less time? We know it’s a difference
of 3 seconds but did she have 3
seconds more or less? Well since she started before
him, she had 3 seconds more. This goes back to the same
warmup problem we did with James and Sylvia where Sylvia
had 30 minutes more because she left before James. It’s the same exact setup and
that’s all you have to do. So when you have a
comparison of time like this, just ask yourself did this
person have more or less? And now we can just distribute. And there’s your distances. Now what’s the relationship? Well if Jimmy takes off after
Sally, Sally already left, he’s got to catch her. And we’re asking how long does
it take for him to catch her, which means their
distances are the same? So if we take our two distances,
we set them equal to each other, this will give us an equation that we can easily
solve and it’s 3. T is time, which is in
seconds so it’s 3 seconds. It will take Jimmy 3 seconds
to catch Sally and that’s it. Alright so these are the three
different types you’re going to have for our basic
word problems that involve uniform motion. They will get a little bit
trickier as you get to the very, very last problems
in our section. But these are our basic setup. So if they’re going
towards each other, you add the two distances
together to make that total distance. If they’re going away from each
other you do the exact same thing because they will
travel some total distance from here to there. And if they’re going in the
same direction it’s usually when will they catch each other
so that’s when they’re equal. Alright so give this one a shot. I’ve already got
the picture for you. All you have to do
is fill everything in and then see what
the relationship is. So hit pause and give it a shot. And there’s the answer. So they gave us a nice little
hint where it said same time. So if you know the time is the
same you can make t the same. And we just plug in our
speeds, use the formula and since they’re going
in opposite directions, there’s a total distance given. So these 2 have to add up
to that total distance. So we know that that’s 85t and
that’s 95t for our distances and they have to add up to 315. Alright turn the page,
let’s try another. Give that one a shot. Hit pause now and try it. Ok and before you
start this one, make sure that you simplify your
time and simplify your time. This is not minutes
that we want. We want hours because
this is miles per hour. And we have to make
sure that they match. So now give it a shot. Alright and that’s how
you should have filled it in so those are your
2 distances. And now what’s the
relationship between them? So since they’re going in the same direction you’re
going to set them equal. So set them equal and solve it. Alright so we should
have the cars traveling at 36 miles per hour but
distance he travels to work. So you can plug it
in here or here. I’m going to plug it in the 1st. So 0.5 times, this is our
distance, 0.5 times 36, that’s half of 36
so it’s 18 miles. That’s his distance
to work, 18 miles. Alright, give the
next one a shot. All the way through, I’m not
going to help at all this time. Just write the answer
in about two seconds. Alright so you should
have got 1.5 hours. And since they started
at 1:00 pm that would give us
a time at 2:30 pm. Alright I think you got
the idea but I just want to do one more together
just to make sure. Alright so this is how
they should be done. Now you’re not going to
even have this on your paper when you’re doing these. You’ve got to set
them up all yourself. No more pictures. So 2 planes start from
the same point and fly in opposite directions. So you have to draw
the picture now. It’s very important to get an
idea what the relationship is. So 2 planes fly in
opposite directions. So we know it’s a type
where we’re adding them up and there it is, total
1400 miles apart. So we know that we’re going
to equal 1400 at some point. Ok the first plane is flying
50 miles per hour slower than the second plane so
we’ll say plane 1, plane 2. And it’s flying at 50 miles, the first plane is 50
miles per hour slower. That means we have
to take it away. In 2.5 hours, so we’re assuming
they left at the same time, which they did, so
2.5 is our time. We use our formula and
then those 2, the decimal, have to add up to 1400. So solve it and so we should
get an x of 305 miles per hour and that’s for plane 2. So plane 2 is traveling
at 305 miles per hour. And plane 1 is traveling
at 50 miles per hour slower so 255 miles per hour. Alright and then
now we just have to check it the same way
we checked it before. So we have this speed
times the time and this speed times the time and we should have the
total distance there. So if we have 305 miles per hour for 2.5 hours plus 255 miles
per hour for 2.5 miles, that should give us a
total distance of 1400. Plug it in. [ Silence ] Fourteen hundred, checks out. And that’s it. That’s uniform motion. Thank you.