Bunuel wrote:
In the figure above, car A and car B travel around a circular park with a radius of 20 miles. Both cars leave from the same point, the START location shown in the figure. Car A travels counter-clockwise at 60 miles/hour and car B travels clockwise at 40 miles/hour. Car B leaves 20 minutes after car A. Approximately how many minutes does it take for the cars to meet after car A starts?
A. 63
B. 75
C. 83
D. 126
E. 188
Kudos for a correct solution. 800score Official Solution: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 towards each other.
A [ ______________________ ] B
We start by solving for the circumference of the park:
C = 2πr.
Plugging 20 into the equation, we get:
C = 2 × 3.14 × 20 = 125.6 miles.
To calculate how long it takes the cars to meet, use the variable T as the time, in hours, that it takes for the cars to meet after car A starts.
When the cars meet, car A will have traveled 60T miles (distance = rate × time) and car B will have traveled 40 × (T – (1/3)) miles (since it left 20 minutes later, it will have been traveling 1/3 of an hour less). Furthermore, the distance both cars will travel combined is 125.6 miles. So we have the equation:
Total Distance = Distance A travels + Distance B travels
125.6 = 60T + 40(T – (1/3))
125.6 = 100T – (40/3).
Then we have approximately: 139 = 100T. So, T = 1.39 hours.This is equivalent to 1.39 × 60 = 83 minutes.
The correct answer is choice (C).