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Description:

Two birds are migrating due north. The first bird flies at a rate of 35 miles per hour. It will eventually migrate on the same path as the second bird, which begins its journey 45 miles directly north of the first bird. The second bird flies at an average speed of 20 miles per hour. Assuming that both birds begin flying at the same time, if t represents the amount of flight time in hours, which inequality represents the length of time that the first bird is ahead of the second bird?


Transcript

00:02

Okay shmoop furs Just two more math questions in this

00:04

section Review our little formula sheet here right there All

00:09

right let's Get into it to birds are migrating due

00:11

north First flight five thousand Eventually something passes The secondary

00:14

begins its journey forty five mile directly north of the

00:15

first bird Second replies an average of twenty miles an

00:17

hour flying thing kind of representing flight time hours which

00:20

inequality represent the length of time for the first bird

00:22

gets ahead of second All right great question here All

00:27

right We're going to need a little bit of modeling

00:28

a little bit of chart in here So let's think

00:30

about it The birds flights can be modelled as a

00:32

linear equation on a graph with the speeds being the

00:36

slopes of those lines And we need to account for

00:39

the fact that the second bird is forty five miles

00:42

ahead at the beginning So these air the equations for

00:45

the distances traveled by the two birds right Burn one

00:49

is just thirty five t right it's house fast she's

00:52

going and bird two is twenty plus forty five A

00:55

little bit ahead Remember they're going both due north this

00:58

kind of complex and you've got to really think about

01:00

where these lines are going to intersect All right well

01:03

we cleverly named the bird's bird one and bird to

01:05

hopefully they don't get offended We can only use the

01:07

information we're given notice that bird one is initially behind

01:11

right here But after the grafts intersect in the two

01:14

birds high five in the air ever rooms do with

01:17

their wings Bird one pulls ahead of bird to there's

01:20

a way to represent Their flight paths algebraic li the

01:23

question asked for wind bird one is ahead of bird

01:27

too So set the equation inverted one to be greater

01:30

than that of bird too So we get thirty five

01:33

t is greater than twenty plus forty five Now we

01:36

isolate the t yeah we're going fast here We know

01:39

but the is testing whether you showed up in school

01:41

that day so isolate t we got thirty five t

01:43

minus twenty is greater than forty five and you can

01:46

treat these greater than things like their equal things and

01:49

we've got fifteen tea then right Thirty five hundred twenty

01:51

fifteen so fifteen tea is greater than forty five so

01:54

tea is greater than three So what does that mean

01:56

While the inequality that represents the length of time that

01:59

the first bird is ahead of the second bird is

02:01

t is greater than three so it's just a if

02:05

we worried to distraction over the thought of the two

02:08

birds colliding in midair we may have subtracted thirty five

02:11

miles an hour from the initial forty five mile advantage

02:13

but we can't do that because they're both headed north

02:16

from presumably different directions There or calculated the difference between

02:20

the two speeds which on its own doesn't help us

02:22

And both of these answers would have been incorrect So

02:24

yeah it's a And uh just beware of the birds 00:02:28.148 --> [endTime] hitting each other That would be sad

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