Question

in still air a bird flies 36 miles per hour with the wind it travels 6 miles farther in 3 hours then it flies in 6 hours against the wind, in miles per hour? round your answer to the nearest tenth

Answer 1

Let v be the speed of wind.

1. With the wind a bird flies 3 hours. The speed of bird with the wind is 36+v mi/h.

Then it flies the distance

`(36+v)\cdot 3` miles.

2. Against the wind a bird flies 6 hours with the speed 36-v, then it flies the distance

`(36-v)\cdot 6` miles.

3. If with the wind a bird travels 6 miles farther than against wind, you have an equation

`(36+v)\cdot 3=(36-v)\cdot 6+6.`

4. Solve it

`108+3v=216-6v+6,\\ \\9v=222-108,\\ \\v=(114)/(9)=(38)/(3)\approx 12.7`

5. You find the speed of the wind
`v=(38)/(3)\approx 12.7` mi/h. Then a bird:

• has speed
  `36-12.7=23.3` mi/h against the wind;
• has speed
  `36+12.7=48.7` mi/h with the wind;
• flies distance
  `(36+v)\cdot 3=\left(36+(38)/(3)\right)\cdot 3=108+38=146` miles with the wind;
• flies distance
  `(36+v)\cdot 3=\left(36-(38)/(3)\right)\cdot 6=216-76=140` miles against the wind.