I have tried numerous ways to solve

Question

On a certain day, Donnie observes the wind is blowing at 4 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 6 minutes later. What is the airspeed of the bird?

Answer 1

Hi Jacuelyn,

 

Let's begin by writing expressions for the bird's air speed (r) with the wind and against the wind:

    r + 4 (bird's air speed with the wind)

    r - 4 (bird's air speed against the wind)

 

Next, let's write an equation expressing the bird's total flight time as equal to the bird's total flight distance divided by the bird's average air speed (with and against the wind):

    [3/4 + 3/4] / [((r + 4) + (r - 4)) / 2] = 6/60

    1.5 / (2r/2) = 1/10

    1.5/r = 1/10

    (1.5)(10) = (r)(1)

    r = 15 mph (bird's air speed)

 

Finally, we can verify our answer by plugging it back into the equation to see if both sides prove equal:

    [3/4 + 3/4] / [((r + 4) + (r - 4)) / 2] = 6/60

    [3/4 + 3/4] / [((15 + 4) + (15 - 4)) / 2] = 1/10 

    1.5 / [(19 + 11) / 2] = 1/10

    1.5 / (30/2) = 1/10

    1.5 /15 = 1/10

    15(1.5/15) = 15(1/10)

    1.5 = 15/10

    1.5 = 1.5 (both sides proven equal)

 

Since both sides of the equation have been proven equal with our answer plugged in, we are confident that our answer is correct.

 

Thanks for submitting this problem and glad to help.

 

God bless, Jordan.