pls help...me solve this?

Question

With a tail wind, a plane flew 120 miles in half an hour. Returning against the wind, the trip took 45 minuts. find the plane's speed (in mi\ h) in still air and the wind speed.

When i tried to solve this i got
planes speed 90
and wind speed 30
is this correct? if not how do i get the correct answer?

Answer 1

Okay, look at it this way.

Let the speed of the plane be P and that of the wind be W.

Now, when a plane travels with a tail wind, the effective speed becomes P+W. The plane travels 120 miles in half an hour at a speed of (P+W), which means in one hour it travels 240 miles. The equation that you get for this will be P+W = 240 (take this as equation 1).

When the plane travels against the wind, the effective speed becomes P-W. It takes 45 minutes to complete 120 miles, which translates to a speed of 160 miles per hour. How do you get this?

Speed = Distance/time
P-W = (120/45) * 60 (multiply with 60 so that you can get the speed per hour.
= 160 mph

P-W = 160 is your equation 2

P+W = 240 ---------------------1
P-W= 160 -----------------------2

Adding both equations, you will get 2P = 400, P=200.
Substituting in one of the equations in place of P, you get W as 40.

Speed of the plane is 200 mph. Windspeed is 40 mph

Answer 2

If you want to solve it arthmetically and it is easier,here is the solution
Plane speed+wind speed=120/(1/2)=240
Plane speed-wind speed=120/(3/4)= 160
(Adding The two and dividing by 2,we get the speed of the plane is200 miles/hr
Subtracting and dividing by 2,we get the wind speed as 40 miles/hr.
Algebrically,we have to follow the proess given below
Let the speed of the plane and that of the wind be x mph and y mph
According to the problem.
x+y=120/1/2=240.......(eqn 1) [Speed=Distnce/Time]
x-y =120/3/4= 160 (eqn 2) [45 minutes=3/4 hr]
adding eqn 1 and 2,we get
2x=400
=>x=400/2=200
Putting the value of x in eqn 1,we get
200+y=240
=>y=240-200=40
Therefore,the speed of the plane is 200 mph and that of the wind is 40 mph

Answer 3

distance = velocity * time
d = v * t
First trip; d1 = 120 miles,
velocity 1 = plane speed +wind speed, let this = x + w
t1 = 0.5 hours
so 120 = (x+w)*0.5
240 = x+w
w = 240 - x

Second Trip
d2 = 120 miles,
velocity 2 = plane speed -wind speed, let this = x - w
t2 = 0.75 hours
so 120 = (x-w)*0.75
160 = x - w

Substitute in w = 240 - x
and then
160 = x - 240 + x
2x = 400
x = 200 miles / hour

From w = 240 - x
w = 240 -200 = 40 miles per hour

Check: 120 = (x-w)*0.75 = (200-40) x .75 = 120 ok

Answer 4

let p = speed of the plane in still air
let w = speed of the wind
120/(p + w) = 1/2 hr
120/(p - w) = 3/4 hr
p + w = 240 mph
p - w = 160 mph
2p = 400 mph
p = 200 mph
w = 40 mph

Answer 5

the formula for speed is travelled distance/ time taken
so, you travel 120 miles in 30 minutes, so one minute you had travelled 4 miles. total time taken is 30 + 45 = 75 minutes, so converted to hour, will be 75/60 or 1.25 hours or 1/1/4 hours. total distance = boarding + returning, so 120 + (45 X 4) = 300 miles. therefore, the speed will be 300 divided by 1.25 = 240 mi/h

Answer 6

in still wind the speed is 120m per half hour so it is 240m per hour.
in wind every 120 miles takes 45mites
so every x miles takes 60 mites which is one hour
so x=120*60/45=120*12/9=120*4/3=160 miles per hour
so the speed 240 and 160

Answer 7

Let x be the speed of the airplane and y the wind's.

x+y = 240
x-y = 160
x=240-y
x=160+y

I'll let you figure it out from here.