Need Math help pls...?

Question

can u help me answer this question, i do not understand what to do.

A plane Flying against the wind took 6 hours to complete a 720 mile trip. On the return flight, flying with the wind, the plane took only 4 hours. Find the plane's speed in still air and wind speed.

Answer 1

speed = distance / time
speed against wind = 720 / 6 = 120 Mph
speed with wind = 720 / 4 = 180 Mph

if the speed of the air and the plane is the same each time
so the speed of the plane is the mean value of the both case

speed in still air = (180 + 120) / 2 = 300 / 2
speed in still air = 150 Mph
and the wind speed = (180 - 120) / 2
= 30 mph

Answer 2

Firstly, remember that distance = rate * time.

Flying against the wind, we have:
720 = (s - w)*6, where s is speed in still air and w is wind speed.
Flying with the wind, we have:
720 = (s + w)*4.

Distribute in each equation and you have a system:
720 = 6s - 6w
720 = 4s + 4w
Multiply the top equation by 2 and the bottom by 3
1440 = 12s - 12w
2160 = 12s - 12w
Add the equations:
3600 = 24s, now divide both sides by 24.
s = 150. Plug this back into and equation:
720 = 4*150 + 4w
720 = 600 + 4w
120 = 4w
w = 30
So, the speed of the plane in still air is 150 mph
and the wind speed is 30 mph

Answer 3

Let the Plane's speed be x mph and that of the wind be y mph
By the problem,
x-y=720/6=120 [speed= distance/time]
x+y=720/4=180
Adding,we get
2x=300
=>x=300/2=150
Putting the value of x in the second equation,
150+y=180
=>y=180-150=30
Therefore,the speed of the plane and the wind is 180 and 30 miles/hour respectively
(Please note that I live in India and is generally on line between7 am and 10 am Indian Standard time in the morning and between 6 and 9 pm in the evening.if you post your question during this period,I assure you to give a quicker answer.Sorry for the delaythis time)

Answer 4

Ok, so we know the 720 miles took 6 hours with the planes still air speed, x, subtracting the wind speed, y.

So, for the trip 720 / (x - y) = 6

Thus, the trip back was 720 / (x + y) = 4 because the planes still air speed, x, was combined with the wind speed, y.

So now we have two equations that we can use substitution on to see for what two values of x and y satisfy both equations.

Firstly, 720 / (x - y) = 6, lets solve this for x.

Multiply both sides by (x - y)

720 = 6(x - y)

Now divide by 6

120 = x - y

Add y to both sides

x = 120 + y

Now we substitute this value of x into the other equation

so 720/ (x + y) = 4, now becomes

720 / ( ( 120 + y) + y ) = 4

Notice x became 120 + y

So now we have 720 / ( 120 + 2y) = 4

Multiply both sides by (120 + 2y)

720 = 4(120 + 2y)

Divide both sides by 4

180 = 120 + 2y

Subtract 120 from both sides

60 = 2y

Now divide both sides by 2

y = 30

So the wind speed was 30

Now we can take this 30 and find the plane's still air speed by plugging it into one of the previous equations

So,

720 / (x + 30) = 4

Multiply both sides by (x + 30)

720 = 4(x+30)

Now divide both sides by 4

180 = x + 30

Subtract 30 from both sides

x = 150

So the plane's still air speed is 150

So,

The plane's still air speed = 150 mph
The wind speed = 30 mph

Answer 5

The plane was traveling into the wind at 120 mph (720 miles/6 hrs.) and was traveling with the wind at 180 mph (720/4).

So, let x = the plane's speed, and y = wind's speed.

x + y = 180 (plane going with the wind)
x - y = 120 (plane going against the wind)

Using substitution, you get x = 180 - y, then (180 - y) - y = 120

180 - 2y = 120

-2y = -60

y = 30

The wind speed is 30 mph. Subbing into one of the top equations, the plane's speed is 150 mph.

Answer 6

Speed Against the wind = 720/6 = 120mph
Speed With the wind = 720/4 = 180mph
Plane Speed = x = 150 mph

120+x=180-x
2x=300
x =150 mph

Wind speed = 180-150 = 30 mph

Answer 7

let p be the speed of the the plane and w be the speed of wind.

it plane go against the wind:
(p - w)6 = 720

now the plane flies with the wind:
(p+w)4 = 720

p+w = 180
p = 180 - w

(180 - w - w)6 = 720
180 - 2w = 120
-2w = -60
w = 30mi/hr

p = 180 - 30 = 150 mi/hr

hope this helps

Answer 8

let a = speed of plane
let b = speed of wind

(a+b) 4 = (a-b) 6
4a + 4b = 6a - 6b
10b = 2a
a=5b

(5b+b)4 = 720
6b = 180
b = 30 mph , speed of wind

a = 5(30)
a = 150 mph, speed of plane in still air

Answer 9

let plane speedin still air be=x
let air speed be=y
case 1:
(x-y)*6=720
case 2:
(x+y)*4=720

solving 1&2
24x=1440+2160
24x=3600
x=150mile/hour y=30mile/hr

Answer 10

s1= plane speed
s2= wind speed
d =720 mile
t1= 6h (time);t2=4h
d=s*t
(s1-s2)*t1=d; s1-s2=120 miles/h
(s1+s2)*t2=d; s1+s2=180miles/h
2s1=300miles/h=>
s1=150miles/h
s2=30miles/h