Distance Problem?

Question

An airplane travels 800 miles against the wind in 4hrs and makes the return trip with the same wind in 2hrs. Find the speed of the wind.

Answer 1

Call the speed of the airplane v.

Call the speed of the wind w.

The net speed of the airplane on the first trip is thus (v-w) and the net speed of the airplane on the second trip is (v+w).

Recall that:

distance / speed = time

So call the distance the airplane travels on each trip d where d = 800 miles. Then the first trip gives us:

d/(w-v) = ( 4 hours )

and the second trip gives us:

d/(v+w) = ( 2 hours )

In other words:

d/(v-w) = 2*d/(w+v)

which means we can cross-multiply:

(v+w)*d = (v-w)*2*d

vd + wd = 2vd - 2wd

3wd = vd

or:

v = 3*w

Now you can solve for the speed of the wind.

(4 hours) = d/(v-w) = d/(3w-w) = d/(2w)

which means:

w = d/(2*(4 hours)) = (800 miles)/(8 hours) = 100 miles per hour

So the speed of the wind is 100 miles per hour.

The speed of the plane is 300 miles per hour.

Note that:

(800 miles)/(400 mph) = 2 hours
(800 miles)/(200 mph) = 4 hours

So that works. And your answer is 100 miles per hour.

Answer 2

Against the Wind

800 miles / 4 hrs = Plane Air Speed - Wind Speed

800 miles / 2 hrs = Plane Air Speed + Wind Speed

Subtacting the 2nd condition from the First Leaves

200 miles/hr = 2 x wind speed

Wind Speed = 100 miles per hour

Plane air speed = 300 miles per hour from condition 1

300 - 100 = 200 mph 800/4
300 + 100 = 400 mph 800/2 satisfies both conditions OK

Answer 3

Let
w = speed of the wind
a = speed of the airplane

Thus,
a + w = speed of the airplane with the wind
a - w = speed of the airplane against the wind
2 hrs = time of the airplane with the wind
4 hrs = time of the airplane against the wind

Since d = rt,
2(a + w) = distance
4(a - w) = distance

Since
distance = 800,

then we have the system of equations
2(a + w) = 800
4(a - w) = 800

Divide
a + w = 400
a - w = 200

Multiply the 2nd equation by -1
a + w = 400
-a + w = -200

Add the equations
2w = 200

Thus,
w = 100

Therefore, the speed of the wind is 100 miles per hour.

^_^

Answer 4

Equation 1.
800 = (P - W)4
200 = P - W

Equation 2.
800 = (P + W)2
400 = P + W

Adding Equations 1 + 2.
600 = 2P
P = 300

Substituting P to Equation 1.
200 = 300 - W
W = 100

Answers:
Speed of wind is 100 miles/hour
Speed of plane is 300 miles/hour

Answer 5

let speed of wind is =x miles\hr
distance = 800 miles

speed of plane = y miles \hr
y -x =800/4 =200
y+x =800/2=400
x = 100 miles\hr

Answer 6

at first it is physics question not math one !
v:the airplane speed
v':the wind speed
800=(v-v')*4 ==> 4v-4v'=800
800=(v+v')*2==> 4v+4v'=1600
==> 8v=2400 ==> v=300 mile/hr