# 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

it’s not asking for that. It’s asking for the

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.