Head wind tail wind???

[trista654]

With a head wind, a plane traveled 1000 km in 4 hours. With the same wind as a tailwind, the return trip took 3h 20min. Find the plane's air speed and the wind speed.

The problem to start it is:

Tail: (R+W)=1000
Head: (R-W)=1000

4R-4W=1000
10/3R+10/3W=1000

It should be 2 problems and there also should be a check

 

[tkhunny]

With a head wind, a plane traveled 1000 km in 4 hours. With the same wind as a tailwind, the return trip took 3h 20min. Find the plane's air speed and the wind speed.

OK Let's see where you go.

Tail: (R+W)=1000
Head: (R-W)=1000

I know what you MEAN, but you have not written it meaningfully.

Distance = Rate * Time

You have only Rate and Distance. It doesn't make any sense. You do have the rates matched up with the direction. That is good.

4R-4W=1000
10/3R+10/3W=1000

See how you managed to get the right structure even though it didn't exist in the previous display?

It should be 2 problems and there also should be a check

What do you mean? Solve the system. I'd start with multiplying the second one by 3. (Way to go on using the fractions, by the way. They scare most people.)

4R - 4W = 1000
10R + 10W = 3000

Get rid of common factors, 4 and 10

R - W = 250
R + W = 300

Does it look any easier?

 

[trista654]

I dont know how to do it but this is the way my teacher told us to do it. So I dont know my teacher told me that w=25 but I dont know how she got that (I asked her after I tried to solve it so I cant just plug it in I have to show the work on how I got it)

 

[trista654]

WOOHOO
I got it I did something wrong on the second part of it so it messed everything up but I did it thank you though.

 

[tkhunny]

There are lots of ways to solve systems like this.

R - W = 250
R + W = 300

"The Substitution Method"
Solve one for something

R = 250 + W

Substitute into the other

(250+W) + W = 300

And solve for W. R will be easy after that.

 

[Denis]

Just another way to solve:
R - W = 250 [1]
R + W = 300 [2]
-R + W = -250 [3] : multiply [1] by -1
2W = 50 : add [2] and [3]
W = 25

Of course you could subtract [1] from [2] right away and get same thing;
I prefer changing signs and adding: less confusing than subtracting !