In the figure above, car A and car B simultaneously begin traveling ar

Area = 1256 miles = pi * r^2 ---> r=\sqrt{400} = 20 miles

Circumference of the park = 2 * Pi * r = 40*3.14 = 125.6 miles


total speed of the two cars = 100 miles

Time taken for both cars to meet = Distance/speed (hrs)
=1.256 hrs * 60
=75 mins(approximate)


Ans C

OFFICIAL SOLUTION:

(C) 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 into a straight line. Notice that cars A and B are at opposite ends of the line traveling toward each other.

A [ ______________________ ] B

We know that the area of the circular park is 1256 square miles and that the area of a circle is equal to πr². So, 1256 = πr². Divide by 3.14, our approximation of π.

1256/3.14 = 400 = r².r = 20 miles.

Now, solve 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 to meet, combine the speeds of car A and car B to see how long it would take them to travel 125.6 miles.

Car A and car B are traveling toward each other at the rate of 40 + 60 = 100 miles per hour (because they are heading toward each other, we add their speeds together). At 100 mph, it will take them 1.256 hours to travel 125.6 miles and meet up.

Multiply 1.256 hours by 60 (because there are 60 minutes in one hour, and we are looking for the answer in minutes): 1.256 × 60, which is approximately 75 minutes.

The correct answer is choice (C).

distance the cars have to travel = circumference of the circle = 2pir
given area = pir^2=1256
r^2=1256*7/22 = 400
r=20
therefore distance = 2pir=40*22/7= ~126
time taken = relative distance /relative speed = 126/100 = 1.26 hours ~ 1 hour 15 minutes = 75 minutes

Area if the circle,
pi*\(r^2\) = 1256,
\(\frac{22}{7}\)*\(r^2\)=1256
we can generalize 1256 = 8*157, since the options are have a margin of at least 10 points we can write it as 9*154 to ease up the calculations.
\(\frac{22}{7}\)*\(r^2\)=9*22*7
Solving further we get, r=21.

So the time taken (in minutes) by both cars to meet will be:

\(\frac{22}{7}\)*2*21*\(\frac{60}{100}\)

(100 = 40+60, cumulative speed of the cars)

Solving further we get time = 75.6 mins ~ 75 mins

Option C

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