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Cars Y and Z travel side-by-side at the same rate of speed

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Cars Y and Z travel side-by-side at the same rate of speed

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Cars Y and Z travel side-by-side at the same rate of speed along parallel roads as shown above. When car Y reaches point P, it forks to the left at angle x°, changes speed, and continues to stay even with car Z as shown by the dotted line. The speed of car Y beyond point P is what percent of the speed of car Z?

(1) The speed of car Z is 50 miles per hour.
(2) x = 45

OA B
Source: Veritas Prep

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BTGmoderatorDC wrote:


Cars Y and Z travel side-by-side at the same rate of speed along parallel roads as shown above. When car Y reaches point P, it forks to the left at angle x°, changes speed, and continues to stay even with car Z as shown by the dotted line. The speed of car Y beyond point P is what percent of the speed of car Z?

(1) The speed of car Z is 50 miles per hour.
(2) x = 45

OA B
Source: Veritas Prep
I assume that car Y and car Z start from the same points on their respective road at the same time, else the answer would be E.

Since car Y forked out at xº and evened out with car Z as shown in the diagram, car Y must increase its speed; compared to car Z, it traveled a greater distance. Since the question wants an answer in percent, the value of actual speed is redundant data; thus Statement 1 is insufficient.

With the information that xº = 45º, we can certainly determine the proportionate length of the hypotenuse (in terms of the base) of the right-angled triangle, ie., distance from point P till the dotted line. Thus, the two speeds are comparable. Sufficient.

The correct answer: B

Hope this helps!

-Jay
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