Question

A 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

let the speed of bird in still air be x km/ hr

and speed of wind be y km/ hr

when the bird was flying in the same direction as of wind

then relative speed = (x + y) km/hr

when the bird was flying in opposite direction

then ,

relative speed = (x - y) km/hr

since , the distance travelled in both side is same ,

first case , in same direction

Distance = 45km , time = 2 hr 30min

= 2hr + 30/ 60hr = 2.5 hr

relative speed = 45 / 2.5

x + y = 45/ 2.5

x + y = 18 -----(1)

second case , in opposite direction

Distance = 45km , time = 4hr 30min

time = 4hr + 30/60 hr = 4.5 hr

relative speed = distance/ time

x - y = 45/ 4.5

x - y = 10 ---(2)

on adding (1) and (2) , we get

2x = 18 + 10

2x = 28 => x = 14km/ hr

from (1)

x + y = 18 => 14 + y = 18

=> y = 4km/ hr

speed of bird in still air = x = 14 km/hr

and speed of wind = y = 4km/ hr

Answer 2

HERE IS YOUR ANSWER

Let the speed of bird be = x km/hr

So,the speed of wind be = y km/hr

When bird is flying in the direction wind,then the speed is =(x+y)km/hr

When bird is flying in the opposite direction of wind , then the speed is (x+y)km/hr

WE KNOW THAT ,

SPEED=DISTANCE/TIME

So,

When bird is flying in the direction of wind it's speed is

x+y=d/t

x+y=45/2.5

x+y=18-----(1.)

When bird is flying the opposite direction of wind it's speed is

x-y=d/t

x-y=45/4.5

x-y=10-------(2.)

ADDIND EQ.(1.) AND (2.)

x+y+x-y=18+10

2x=28

x=28/2

x=14

From eq.(1.)

x+y=18

14+y=18

y=18-14

y=4

Speed of the bird in still air = 14 km/hr

Speed of the wind =4km/hr