# Thread: DVT word problem help needed

1. ## DVT word problem help needed

A airplane that travels from one city to another city against the wind takes it 4 hours to get there, the voyage back only takes it 2 hours. If the distance between both city's is 600km, what is the speed of the plane?

So far I have:

D = V x T
Go 600 4
Return 600 2

It's a table.

So,

600/4=V
600/2=V

Is this right so far?

2. Originally Posted by Methodd
A airplane that travels from one city to another city against the wind takes it 4 hours to get there, the voyage back only takes it 2 hours. If the distance between both city's is 600km, what is the speed of the plane?

So far I have:

D = V x T
Go 600 4
Return 600 2

It's a table.

So,

600/4=V
600/2=V

Is this right so far?
$\displaystyle 600 = (v - u)(4)$ .... (1)

$\displaystyle 600 = (v + u)(2)$ .... (2)

Equate equations (1) and (2) and simplify: v = 3u.

Substitute v = 3u into either equation (1) or (2) and solve for u. Therefore get v.

I will let you think about which of u or v is the speed of the plane.

3. Originally Posted by mr fantastic
$\displaystyle 600 = (v - u)(4)$ .... (1)

$\displaystyle 600 = (v + u)(2)$ .... (2)

Equate equations (1) and (2) and simplify: v = 3u.

Substitute v = 3u into either equation (1) or (2) and solve for u. Therefore get v.

I will let you think about which of u or v is the speed of the plane.
Ah yes, its coming back now. Thank you very much my good sir!

4. Originally Posted by Methodd
A airplane that travels from one city to another city against the wind takes it 4 hours to get there, the voyage back only takes it 2 hours. If the distance between both city's is 600km, what is the speed of the plane?

So far I have:

D = V x T
Go 600 4
Return 600 2

It's a table.

So,

600/4=V
600/2=V

Is this right so far?
Okay, so the net speed going (against the wind) was 600/4= 150 mph and returning (with the wind) was 600/2= 300 mph. Taking v to be "indicated air speed" (speed of the plane relative to the wind) and w to be the wind speed, we have v- w= 150 and v+ w= 300. Add those two equations to solve for v and subtract them to solve for w.