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 t…

Question

asked Nov 20, 2019 218k views

1 Answer

Hanno · Answer 1 · 2019-11-27T07:07:51+0000

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
mi/h against the wind;
has speed
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.