# Word Problems Uniform Motion Warm Up

>>Alright. This is a uniform

motion problems warm up. So we’re going to get

used to the formula, that is distance

equals rate times time. I have it backwards because

we’re going to plug in the rate and the time and

then multiply them. OK. So Dara is traveling

at 40 miles per hour. That’s our rate. How far will she travel in

six hours, that’s our time, and the whole thing

is to make sure that your times match,

hours, hours. And so when we multiply

them, you get 240, and it’s that unit right there,

which is miles, and that’s it. So how far will she travel

in t hours, same speed, for t would give us 40t, and this is what our

problems are going to look like because we’re

going to be looking for either the rate or the time. OK. So like this one. Jim has been traveling

at x miles per hour, so x. How far will he travel

in six hours in terms of x? Well, that’s 6x. Alright. So let’s now

try it with two people. So Liz is traveling

at x miles per hour. Leeann is traveling at

twice the speed of Liz. So if she, if Leeann,

Liz is traveling at x, Leanne is traveling at 2x. OK. How far will Liz

travel in three hours? So 3 is 3x. Leeann is 2x. How far will she travel? Six x. Twice the speed, twice

the distance in the same amount of time, and that’s it. So this is how it’s going

to look with two problems. You’re going to be

given two values. You plug them in for

each and multiply. Alright. Now this

is the last one that we’re going to

use as a warm up. So it says James and Sylvia,

those are our two people. So we have James and Sylvia. James has been traveling

for 22 miles per hour. Sylvia’s traveling

at 33 miles per hour. James has been traveling

for t hours. So that’s his time. So James is done. He’s at 22t for his formula. Sylvia, though, has a comparison with that t. It says Sylvia

left 30 minutes before James. Well, if she left before

James, here’s Sylvia. She heads out, and

then 30 minutes later, that’s when James starts. So it takes them a

while to catch up, which means he had less time, which means Sylvia

has more time. She can’t put 30 because

that’s minutes, that’s hours. It’s got to be 30 over 60. We don’t want the fraction so we

reduce it, and it becomes 0.5. And so when we multiply it,

it’s 33 times t plus 0.5, and that’s their

distances, their formulas. Alright. So that’s the

basis for all of these, the uniform motion problems. This is our setup. And the main start for all of

it is listing our quantities, and this is what we have.