I am having trouble with this problem I have been trying to work on it for at least an hour now an found nothing. I just need help getting the two equations started. Please and thank you!

Flying with the wind, a bird flew 13mi in half an hour. On the return trip against the wind, it was able to travel only 8mi in the same amount of time. Find the speed of the bird in calm air and the speed of the wind.

I know x is speed of bird in calm air and y is speed of the wind but the things I tried I am not coming up with anything.

Flying with the wind the bird covers 13 miles in 1/2 hour, so it has a ground speed of 26 MPH. This equals the speed of the bird's flying in calm air plus the speed of the wind. Flying against the wind the ground speed is 16 MPH, which is the bird's normal speed in calm air minus the speed of the wind. So you have two equations:

x+y = 26 MPH
x-y = 16 MPH

Now you can solve for x, then y.

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Originally Posted by ebaines

Flying with the wind the bird covers 13 miles in 1/2 hour, so it has a ground speed of 26 MPH. This equals the speed of the bird's flying in calm air plus the speed of the wind. Flying against the wind the ground speed is 16 MPH, which is the bird's normal speed in calm air minus the speed of the wind. So you have two equations:

x+y = 26 MPH
x-y = 16 MPH

Now you can solve for x, then y.

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My teacher gave us the answers which is bird flies 21 mph and speed of wind is 5 mph but I don't understand how you got the 26 and 16.

If the bird flies 13 miles in 1/2 hour, then in a full hour it would fly twice as far, which is 26 miles. Hence its speed is 26 miles per hour. And if it flies 8 miles in 1/2 hour, then its speed is 16 miles per hour.

Do you know how how to solve the two simultaneous equations that I gave you? You will find the answer is x = 21 and y = 5, just as your teacher said.

Quote:

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Originally Posted by ebaines

If the bird flies 13 miles in 1/2 hour, then in a full hour it would fly twice as far, which is 26 miles. Hence its speed is 26 miles per hour. And if it flies 8 miles in 1/2 hour, then its speed is 16 miles per hour.

Do you know how how to solve the two simultaneous equations that I gave you? You will find the answer is x = 21 and y = 5, just as your teacher said.

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I guess I don't know how to do it that way. We have been learning like substitution and elimination methods so this one I don't think is the same.

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Originally Posted by jazzyjo94

I guess I dont know how to do it that way. we have been learning like substitution and elimination methods so this one I dont think is the same.

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Never mind I got it I have to divide by 2.