In the figure above, car A and car B simultaneously begin traveling around a circular road. Both cars start from the same point, the START location shown in the figure. Car A travels counterclockwise and car B travels clockwise. The cars meet after car A travels 40 miles/hour for 2.5 hours and car B travels 6.4 miles/hour for 4 hours. Which of the following is closest to the diameter of the circular road (in miles)? Use 3.14 for π. A. 20 B. 40 C. 60 D. 120 E. 140
(B) First, solve for the circumference of the circular road, which is the combined distance traveled by the two cars from the starting point to the meeting point. To visualize this question, think about a circle as just a line segment joined at its two ends. Let’s first cut the circle at the starting point and make it in to a straight line. Notice that cars A and B are at opposite ends of the line traveling toward each other. A [ ______________________ ] B
After 2.5 hours, and at a rate of 40 mph, Car A has traveled 100 miles east (2.4 × 40 =100). Car B has traveled 4 hours at 6.4 miles per hour: 25.6 miles. So our diagram now looks like this:
_________A, B________ |_100 mi__| |_25.6 mi_|
So the length of the segment is equal to 125.6 miles which is identical to the circumference of the circle we began with. To determine the diameter we simply plug in to the formula C = πD where D is the diameter and C is the circumference and π is about 3.14. We can take C equal to 126 and π to equal 3.14. The diameter is therefore equal to D = C/π = 126/3.14 equals approximately 40. The closest solution is choice (B). ----------
Both cars start simultaneously and car A travels for 2.5 hours, while car B travels for 4 hours, still they meet each other at the same time. This doesn't seem right to me.
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