Airplane question, please help me?

Question

an airplane flies 1062 km with the wind in the same time it takes to fly 738 km against the wind. the speed of the plane in still air is 200 km/hr. find the speed of the wind.

err..can someone answer this question and please include some explanation and solution. thanks!

Answer 1

basic idea is that Distance you can go is a function of the Rate you go at and how long (the Time) you go for.  So you could write that as:

D=R*T   or say it as distance equals rate times time.

You can also manipulate this equation to change which variables are on which side of the equal sign and say:

T=D/R   or say it as Time is distance divided by Rate

Since the problem has two different calculations in which TIME remains the same we should use this form of the equation to use the information in  the problem to create two equal things:

FIRST THING:  If airplane flies 1062km with the wind... we can say that can be written as:

T = 1062km / (Wind_Speed + 200)

meaning... that it takes some amount of time to go 1062km flying with the wind and so the RATE is going to be the wind speed plus the plane speed.

SECOND THING:  If the plan flys 738km against the wind we say:

T=738km / (Wind_Speed - 200)

NOW since we know that the first thing and the second thing are equal to each other since the Time is the same ...

1062km / (Wind_Speed + 200)  =  738km / (Wind_Speed - 200)

Now just multiplying and moving things around.... we can change this equation to :

1062km*Wind_Speed - 1062*200 = 738 * Wind_Speed + 738*200

then moving more things around we get:

(1062 - 738 ) * Wind_Speed =  (738 + 1062) 200

or doing the math:

324 * Wind_speed = 360000

or

Wind_Speed = 360000  / 324  = 1111 and 1/9th

OR SOMETHING LIKE THIS....

didnt' check the math... but the logic is right  

Answer 2

Rate X Time = Distance

So looking at this we have:

(200+Wind) X T = 1062  + wind is with the wind

(200-Wind) X T = 738     - wind is against the wind

Multiplying through we get new equations

200T+TW = 1062

200T-TW = 738

So, adding these simultaneous equations, we get:

200T+200T+TW-TW = 1062+738

400T=1800, T=4.5hrs

So, substitute 4.5 for T and we get:

900+4.5W=1062

4.5W=162

W(Windspeed)=36km/h

900-4.5W=738

162-4.5W=0

162+4.5W

36=Windspeed

Windspeed is 36 k/mh

If you remember Rate X Time = Distance and can express any of those terms and do the math, this type of problem should be easy for   you in the future.

Answer 3

Let the wind speed be V. Then

1062/(200+V) = 738 /(200-V)

Cross-multiply

1062(200-V) = 738 (200+V)

212400-1062V = 147600 + 738V

64800 = 1800V

V=36 km/hr  ANSWER