Flight out of the city!

Algebra Level 4

An airplane, Flying from city A to B, Covers the distance from A to B in $3 \dfrac{1}{3}$ hours and comes from B to A in 4 hours. If the distance Between A and B is 1000 km and the air current is moving from A to B, Find the speed of the airplane in still air.

Answer in m/s

The answer is 76.388.

1 solution

Mehul Arora
May 24, 2015

Let the Speed of the airplane in Still air be $x$

And, The speed of the Air current = $y$

Therefore, $\dfrac{1000}{x+y}= 3 \dfrac{1}{3}$ (Distance per unit speed = time)

$x+y=300$

Here, We add the current and the wind speed because the airplane is moving with the wind velocity.

Similarly, While moving against the current,

$\dfrac{1000}{x-y}=4$

$x-y=250$

Adding both the equations, We get, 2x=550 km/h

x=275 km/h

Now, For conversion into m/s, We multiply by $\dfrac{5}{18}$

$275 \times {\dfrac{5}{18}}$

= 76.388

Cheers! ^_^

Sir , Can you explain me why you multiplied by 5/18? I am a bit weak in conversions.

Nitesh Chaudhary - 6 years ago

First of all, Kindly do not call me sir. I am way too young for it. And also, I don't deserve it.

1 km= 1000m

1 hour= 60*60 = 3600 seconds.

Hence, $\dfrac{1km}{1hr} = \dfrac {1000m}{3600s}$

= $1 km/h = \dfrac{5}{18} m/s$ (We divide the denominator and numerator by 200 to get the fraction to it's lowest form)

Hence, $1 km/h = \dfrac {5}{18} m/s$

And so, We multiply by $\dfrac{5}{18}$

I hope this helps. @nitesh chaudhary

Mehul Arora - 6 years ago

Thanks Sir , my doubt is cleared. You are very intelligent.

Nitesh Chaudhary - 6 years ago

@Nitesh Chaudhary – Please do not call me sir. Please $\ddot\frown$

It is a pleasure to help others. No need to thank me. And, No I am not intelligent.

Mehul Arora - 6 years ago

@Mehul Arora – Ok Ma'am , I have noted your instruction.

Nitesh Chaudhary - 6 years ago

@Nitesh Chaudhary – Just call me Mehul. Please xD

Btw, That was a good one :P

Mehul Arora - 6 years ago

@Mehul Arora – Hi Mehul Ma'am LOL. @nitesh chaudhary Good one. :P

Nihar Mahajan - 6 years ago

@Mehul Arora – I am just joking don't take it seriously please.

Nitesh Chaudhary - 6 years ago

I've done that. Sorry, pls, it was a mistake actually.

Nice solution!!!!

samuel ayinde - 6 years ago

@Samuel Ayinde – Thanks @samuel ayinde . I am glad you liked it. ^_^

Mehul Arora - 6 years ago

Flight out of the city!

The answer is 76.388.

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