In the figure above, car A and car B simultaneously begin travelling..

Given: area of the circle = \(4\pi\) ----> radius of the circle = 2---> circumference of the circle = \(4\pi\)

Let Va and Vb be the speeds of A and B respectively. For 'where' do they meet, we have the following equation : \(Va*T+Vb*T =4\pi\) ---- (1), where T is the time after which they both meet. Per the question, Va.T = ? or Vb.T = ?

Per statement 1, Vb = Va+30. This is not sufficient as this equation with 1 leaves us with 2 equations and 3 variables (Va , Vb, T) We can not isolate Vb.T or Va.T from this. Thus this statement is not sufficient.

Per statement 2, Va = Vb /2 (twice slower = half the speed). Susbstituting this in equation (1) we get, \(Vb*T = 8\pi / 3\) . Thus this statement is sufficient.

Hence B is the correct answer.

From the property of Speed, Distance and Time
For Constant Time
Speed of A / Speed of B = Distance travelled by A / Distance travelled by B

Area of Track = 4π square miles = π*r^2 square miles
i.e. radius = 2
We have the length of Track = 2*π*r miles = 4π

So we only require the ratio of speeds to find the ratio of Distance travelled by them and find their meeting point

Question : Distance of Meeting point along the track = ?

Statement 1: Car B travels 30 mph faster than car A.
This statement provides the difference of speeds but not the ratio of speeds. Therefore,
NOT SUFFICIENT

Statement 2: Car A travels twice slower than car B.
i.e. Speed of B = 2* Speed of A
Ratio of speeds is 2/1
i.e. Ratio of distance covered till they meet = 2:1
i.e. Meeting Point = (2/3)4π = (8/3)π (in Clockwise direction)
SUFFICIENT

Answer: Option B

800score Official Solution:

Knowing the area of the park, we can find its radius (πr² = 4π square miles, so r = 2 miles). Knowing the radius, we can find the length of the road (the circumference, it equals 2πr = 4π miles). 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

Let’s denote the speed rate of car A by x mph and the speed rate of car B by y mph. When they meet, the whole distance will be the sum of the paths they have travelled. Since they’ve started simultaneously, then they both travelled for the same time. Let’s denote it by t hours. This gives us the following relation:
x × t + y × t = 4π

Statement (1) gives us the fact that y = x + 30. The relation transforms into xt + (x + 30)t = 4π. Let’s plug two values to see if we get different results.
If x = 5, then t = π/10. So the cars would travel 5π/10 = π/2 and 35π/10 = 7π/2 miles respectively.
If x = 10, then t = 4π/50. So the cars would travel 40π/50 = 4π/5 and 160π/50 = 16π/5 miles respectively.

As wee see these results define different points along the track. Therefore statement (1) by itself is NOT sufficient.
Statement (2) gives us the fact that y = 2x. The relation transforms into xt + 2xt = 4π. So xt = 4π/3. Therefore we know that car A travells 4π/3 miles and car B travels 8π/3 miles. That gives us the definite point along the track, no matter what the values of x and t are. So statement (2) by itself is sufficient.
Statement (2) by itself is sufficient to answer the question, while statement (1) by itself is not.

The correct answer is B.

Similar questions to practice:
in-the-figure-above-car-a-and-car-b-travel-around-a-circular-park-201795.html
in-the-figure-above-car-a-and-car-b-simultaneously-begin-traveling-ar-190712.html

Hello,

Even with Statement 2 in consideration, the cars will meet at three different points on the circle. Since the question does not ask us about the first meeting point, how can this be answered?

Thanks

In the figure above, car A and car B simultaneously begin travelling around a circular park with area of 4π4π square miles. Both cars start form the same point, the START location shown in the figure, and travel with constant speed rates until they meet. Car A travels counter-clockwise and car B travels clockwise. Where along the track will they meet? (Note: figure not drawn to scale).

(1) Car B travels 30 mph faster than car A.


(2) Car A travels twice as slowly as car B.

It is DS ques.
(1) says speed of A = x mph
B = x + 30 mph

x = 5 , x = 50 will yield diff results respectively.

NS

(2)
it gives comparison of speed.

we know dis = speed * time

we know total dis. ratio of speed, time is same for both. Sufficient.

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