Question

On a certain day, Donnie observes the wind is blowing at 2 miles per hour. A bird nesting near Donnie's house flies three quarters of a mile down the road (in the direction of the wind), turns around, and returns exactly 12 minutes later. What is the airspeed of the bird? (Here, 'airspeed' is the speed the bird can fly in still air.)

Answer 1

The airspeed of the bird is 7.5 miles per hour.

Step-by-step explanation:

The airspeed of a bird can be determined by considering its velocity relative to the ground and the wind speed. In this case, we are given that the bird flies three quarters of a mile down the road (with the wind) and returns in 12 minutes. We need to find the airspeed of the bird, which is its speed in still air.

To find the airspeed, we can use the equation:

Airspeed = (Downwind Distance + Upwind Distance) / Total Time

In this case, the downwind distance is three quarters of a mile and the upwind distance is also three quarters of a mile. The total time is given as 12 minutes, which is equivalent to 12/60 = 0.2 hours.

Substituting these values into the equation:

Airspeed = (0.75 miles + 0.75 miles) / 0.2 hours = 7.5 miles per hour.

Therefore, the airspeed of the bird is 7.5 miles per hour.

Answer 2

Air speed of bird is
`4.17` mph

Step-by-step explanation:

let the speed of the bird in still air be "X"

Speed of the bird when it flies in the direction of flow of wind
`= X+2`

Speed of the bird when it flies in the opposite direction of flow of wind
`= X-2`

The total time taken is equal to
`12` minutes

`= (12)/(60) \\= (1)/(5)` hours

The distance in miles is equal to
`(3)/(4)`
`= 0.75` miles

`(0.75)/(X+2) + (0.75)/(X-2) = (1)/(5)`

On solving the above equation, we get -

`2 X = (X^2 -4)*(1)/(0.75 *5) \\X^2 -4 -0.75 X =0\\X = 4.17`

Air speed of bird is
`4.17` mph