Question

Bird is flying in the same direction as that of wind, covers a distance of 45km in 2hours 30mins. but it takes 4hr 30min to cover the same distance when it flues against the direction of wind. find the speed of in still air and that by wind.

Answer 1

In the above Question , the following information is given -

A Bird, which is flying in the same direction as that of wind, covers a distance of 45km in 2hours 30 mins.

Now ,

It takes 4hr 30min to cover the same distance when it flies against the direction of wind .

To find -

Find the speed of the bird still air and the speed in the wind.

Solution -

Here ,

A Bird, which is flying in the same direction as that of wind, covers a distance of 45km in 2hours 30 mins.

Let the speed of the bird be x kmph and the speed of the wind be y kmph .

Now ,

The speed of the bird is greater than the speed of the wind .

So ,

x > y

So ,

When the bird is flying in the same direction as that of the wind -

=> Net Speed -

=> ( x + y ) kmph

Now ,

Speed = [ Distance / Time ]

In the first case -

Distance travelled by the bird = 45 km

Time taken => 2 hrs 30 mins

=> 2 ( 1 / 2 ) hr

=> ( 5 / 2 ) hr

Speed = 18 kmph .

So , we can write th first equation as -

x + y = 18

So ,

When the bird is flying in the opposite direction as that of the wind -

=> Net Speed -

=> ( x - y ) kmph

Now ,

Speed = [ Distance / Time ]

In the second case -

Distance travelled by the bird = 45 km

Time taken => 4 hrs 30 mins

=> 4 ( 1 / 2 ) hr

=> ( 9 / 2 ) hr

Speed = 10 kmph .

So , we can write th second equation as -

x - y = 10 .

Thus , we have obtained the following two equations -

x + y = 18

x - y = 10

Adding them

=> 2x = 28 kmph

=> x = 14 kmph

=> y = 4 kmph

Hence , the required speeds of the bird and the wind are 14 kmph and 4 kmph respectively ...

_________

Answer 2

$\huge\sf\pink{Answer}$

☞ Speed of bird in still air = 14 km/h

☞ Doped of wind = 4 km/h

$\rule{110}1$

$\huge\sf\blue{Given}$

✭ Direction of a flying bir and the direction of wind is the same

✭ It covers 45 km in 2 hours

✭ But when it flies in the opposite direction it takes 4 hour 30 minutes

$\rule{110}1$

$\huge\sf\gray{To \:Find}$

☆ Speed of bird in still air?

☆ Speed of wind?

$\rule{110}1$

$\huge\sf\purple{Steps}$

Let speed of bird be x km/h

Let speed of wind be y km/h

➢ Speed of bird in the direction of wind = (x+y)km/h

➢ Speed of bird when it flies opposite to the wind = (x-y)km/h

Speed of a body is given by,

$\underline{\boxed{ \red {\sf Speed = \frac{Distance}{Time}}}}$

Substituting the given values,

Case 1

➝ $\sf x+y= \bigg\lgroup\dfrac{45}{2.5}\bigg\rgroup$

➝ $\sf x+y = 18 \qquad -eq(1)$

Case 2

➳ $\sf x-y = \bigg\lgroup\dfrac{45}{4.5} \bigg\rgroup$

➳ $\sf x-y = 10\qquad -eq(2)$

Adding eq(1) and eq(2),

➢ x+y+x-y = 18+10

➢ 2x = 28

➢ $\sf x = \dfrac{28}{2}$

➢ $\sf\green{x = 14}$

From eq(1)

➠ 14 + y = 18

➠ y = 18 - 14

➠ $\sf\orange{y = 4}$

$\rule{170}3$