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 ...

Why do we assume that both cars complete the circumference? Can't they meet somewhere along the path (without completing the whole track?)

They do meet somewhere along the track. We do NOT assume that EACH car completes the circumference.
They start from the same point and move towards each other along the circumference. It's inevitable that they meet. When they do - each car will travel a path of an arc from the starting point till the meeting point. These two arcs make the circumference, since the edges are the same points.