Word Problems Uniform Motion Warm Up

# 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.