As shown in the figure above, car A and car B simultaneously begin traveling around a circular park with an area of 1256 square miles. Both cars leave from the same point, the START location in the figure. Car A travels counter clockwise at 40mph and car B travels clockwise at 60mph. approximately how many minutes does it take for the cars to meet?

My question is:
How come the equation is incorrect when you add 20 minutes to Car A =
instead of subtracting it from Car B? My equation was 60(T+(1/3))+40T=3D125.6. =20

Hey AEK !

Its because they are not traveling at the same rate. Here is the right way to solve this problem:

The first step is to reduce the circle to a line. We know the length of the line by using the circumference of the circle. So essentially, we want to visualize two cars traveling toward each other in a linear path. We begin by finding the radius of the circle.

Since the area is equal to 1256, we have the following: R^2 = 1256/pi = 400 => R = 20 (aprox.) Now we need to find the length of the path, the circumference. Recall that C = 2piR = 125.6.

Now Car A and B are traveling toward eachother at 40 + 60 = 100mph. So the distance between them is closing at a rate of 100mph. And at 100mph, it will take (v = d/t) 125.6/100mph = 1.256 hours to meet. So, lets convert 1.256 hours to minutes: 1.256 hours x 60 min/hr = 75 min (aprox.)

I hope this was helpful,
Steve

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Now Car A and B are traveling toward eachother at 40 + 60 = 100mph. So the distance between them is closing at a rate of 100mph. And at 100mph, it will take (v = d/t) 125.6/100mph = 1.256 hours to meet. So, lets convert 1.256 hours to minutes: 1.256 hours x 60 min/hr = 75 min (aprox.)"

the correct answer is 83 minutes ...