Question

An airplane flying with a tail wind can complete a journey of 3500 kilometers in5 hours. flying the reserve direction, the plane completes the same trip in 7 hours. what is the speed of the plane in still air??

Answer 1

Reverse direction*

Answer 2

Think about it this way: There are basically two variables. We don't know the speed of the plane without wind, and we don't know the speed of the wind.
Let's call the plane's normal speed S
Let's call the speed of the wind W

When the wind is moving with the plane, it makes the plane go faster, so the speed will be
S+W
When the wind is moving against the plane, it slows it down, and the speed will be
S-W

Answer 3

Now, you should know that
\[\frac{\text{distance}}{\text{speed}} = \text{time}\]

So use that two write two equations representing the two trips.

Answer 4

ok

Answer 5

Can I see your equations?

Answer 6

well im stuck that is why i wanted to see if someone can show me step by step, I know that the answer is 600 kilometers per hour, but idk how to get there

Answer 7

Writing the two equations is step 1 =)

Answer 8

ok can you hold on for a min

Answer 9

Walk through this with me. You can write these two equations.

\[\frac{\text{distance}}{\text{speed}} = \text{time}\]

Answer 10

Gladly =)

Answer 11

ok so the first step is find distance/speed= time?

Answer 12

?

Answer 13

are u there?

Answer 14

To write an EQUATION by using that fact. We have two situations the trip there and the trip back. Start with the trip there. Figure out what to put in as the distance, the speed, and the time.

Answer 15

time= 5

Answer 16

distance and speed idk

Answer 17

???

Answer 18

lol maybe..goshh i really need help :(

Answer 19

You need to come up with 2 equations. You're given enough information to complete the first equation which is for the first trip:\[Speed=\frac{distance}{time}=\frac{?}{?}\]

Answer 20

yeah, is time 5 hours?

Answer 21

Yes. @colombianita19 : sorry for butting in...thought you left. Please continue :)

Answer 22

err I meant @SmoothMath

Answer 23

did he leave?

Answer 24

It looks like he's in the room but maybe afk.

Answer 25

So what does your first equation look like?

Answer 26

is it speed= distance/ time

Answer 27

Yes...plug in the values and solve for the speed. That's the first part.

Answer 28

Distance is also given... if you read the problem.

Answer 29

is the value for time= 5hours?

Answer 30

And for speed, go back and read my first post.

Answer 31

yes

Answer 32

<backing out since Smooth is back>

Answer 33

distance is 3500 kilometers?

Answer 34

for speed is just s?

Answer 35

Yes, 3500km, and that's the same for both situations, right?

Answer 36

Shane, go ahead and take over. I'm distracted.

Answer 37

there and back?

Answer 38

Ok...here's your first equation:\[Speed=\frac{3500km}{5hr}\]So what's the speed?

Answer 39

is it just s? doesn't say

Answer 40

Look at what I just wrote and solve for the speed :)

Answer 41

700?

Answer 42

Yes... So during the first trip the plane with the tailwind traveled at 700km/hr.

Answer 43

Now for the return trip. What do you think the formula will look like for that trip?

Answer 44

time/ distance?

Answer 45

No...it's the same formula: \[Speed = \frac{distance}{time}\]Now plug in what you know for the return trip: It has the same distance which is 3500 km...and it took them 7 hours to return. So what's the speed on that leg of the trip?

Answer 46

<The goal here is to find the difference in speed between both legs of the trip...so you find the speed on each leg and then calculate the difference>

Answer 47

is speed 500?

Answer 48

Yes. So they went 700 km/hr to get there...WITH a tailwind...and they went 500 km/hr to return WITHOUT a tail wind. So what was the speed of the tailwind?

Answer 49

600?

Answer 50

200

Answer 51

Oops...just noticed I made a silly mistake. You were sort of right.

The speed of the plane in still air is 600 km/hr. When it has a 100 km/hr tailwind it goes 700 km/hr...and when it goes back the other way it has a 100 km/hr headwind...which slows it down to 500 km/hr.

Answer 52

on the back of the book is said that the answer is 600 kilometers per hour

Answer 53

600 is right...see what I just wrote.

Answer 54

so what part of the equation did we make the mistake

Answer 55

trip there i have 350/ 5 hrs speed = 700....and trip back i have 3500/7hrs= 500

Answer 56

opsss i mean 3500 on both equations

Answer 57

MY mistake was forgetting about the headwind on the way back.

What this problem boils down to is calculating the difference in speed which I hope you know how to do now. There was a 200 km/hr difference in speed between flying with a tailwind and flying against a headwind. The speed of the plane will actually be in the middle....600 km/hr.

Answer 58

ok thanks! :)

Answer 59

I hope I didn't totally confuse you :) your welcome

Answer 60

*you're

Answer 61

no you are fine! :)

Answer 62

Thanks for askin' before takin' over, Shane. Totally considerate of you. You're a champ.

Answer 63

thanks for trying to help smoothmath:)

Answer 64

Aw, you're sweet. My pleasure =)