# DVT word problem help needed

• Jan 13th 2011, 02:29 PM
Methodd
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?
• Jan 13th 2011, 02:37 PM
mr fantastic
Quote:

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?

$600 = (v - u)(4)$ .... (1)

$600 = (v + u)(2)$ .... (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.
• Jan 13th 2011, 02:42 PM
Methodd
Quote:

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

$600 = (v + u)(2)$ .... (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!
• Jan 13th 2011, 04:27 PM
HallsofIvy
Quote:

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.