Question

I need the explanation of answer #11. On the textbook answer key section is states that the answer to this problem is 300mph. I do not know how to start the problem out. This question is an algebra question with the need to use a quadratic equation.

Answer 1

300 mph

Explanation:

Let's say x is the speed of the plane in still weather.

The time it takes flying against the wind is:

990 mi / (x − 30 mph)

The time it takes flying with the wind is:

990 mi / (x + 30 mph)

The total time is 6⅔ hours, so:

6⅔ hr = 990 mi / (x − 30 mph) + 990 mi / (x + 30 mph)

6⅔ = 990 / (x − 30) + 990 / (x + 30)

20/3 = 990 / (x − 30) + 990 / (x + 30)

Solving this equation for x, multiply both sides by 3 (x − 30) (x + 30):

20 (x − 30) (x + 30) = 2970 (x + 30) + 2970 (x − 30)

20 (x² − 900) = 2970x + 8910 + 2970x − 8910

20x² − 18000 = 5940x

20x² − 5940x − 18000 = 0

x² − 297x − 900 = 0

Factor:

(x − 300) (x + 3) = 0

x = 300 or -3

Since x must be positive, x = 300 mph.