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Martha takes a road trip from point A to point B. She drives x percent of the distance at 60 miles per hour and the remainder at 50 miles per hour. If Martha's average speed for the entire trip is represented as a fraction in its reduced form, in terms of x, which of the following is the numerator?

(A) 110
(B) 300
(C) 1,100
(D) 3,000
(E) 30,000

Respuesta :

Answer:

The correct option is E) 30,000.

Step-by-step explanation:

Consider the provided information.

Let D is the distance between point A and point B.

Let she drive x percent of distance at 60 miles per hour.

That means time taken is: [tex]\dfrac{\frac{x}{100}\times D}{60}[/tex]

Let she drive remaining distance at 50 miles per hour.

That means time taken is: [tex]\dfrac{\frac{1-x}{100}\times D}{50}[/tex]

Average speed = [tex]\frac{\text{Total distance}}{\text{Elapsed Time}}[/tex]

[tex]\frac{D}{\dfrac{\frac{x}{100}\times D}{60}+\dfrac{\frac{100-x}{100}\times D}{50}}=\dfrac{1}{\dfrac{x}{6000}+\dfrac{100-x}{5000}}\\\\\\=\dfrac{1}{\dfrac{5x+6(100-x)}{ 30,000}}\\\\\\=\dfrac{30000}{5x+6(100-x)}[/tex]

[tex]=\dfrac{30000}{600-x}[/tex]

Hence, the correct option is E) 30,000.