AbhishekRyu wrote:A plane named "ship" is flying in a clockwise circular path above Town X. A plane named "car" is also flying in a clockwise circular path above town X at a different altitude and speed from Plane named ship. If the circumference of the path of plane Ship is equal to the circumference of the path of plane Car, and at 5 pm are directly above the same location over town X, how many circular paths must the planes make so that both planes are directly above the same location at the same time above Town X.

1. The circumference of the circular path traveled by both planes is 4 pi miles ( pi = 3.14)
2. The plane ship travels at a constant rate of 1818 of the length of circular path per hour, and plane car travels at a constant rate of 1616 of the length of circular path per hour.

Say when the planes are directly above the same location at the same time above Town X after 5 pm, the plane Ship makes n circular paths and Car makes m circular paths. Also, the speed of Ship is S and that of Car is C.

The minimum value of (n + m) would give us the time when for the first time after 5 pm, the two planes would be together.

Thus, the time taken by Ship to make n circular paths = the time taken by car to make m circular paths

=> (2Ï€r*n) / S = (2Ï€r*m) / C

n/S = m/C

If we get the values of S and C, we can get minimum values of n and m, thus the minimum value of (n + m).

Let's take each statement one by one.

1. The circumference of the circular path traveled by both planes is 4 pi miles. ( pi = 3.14)

We do not need the value of circumference of the circular path. Insufficient.

2. The plane ship travels at a constant rate of 1818 of the length of circular path per hour, and plane car travels at a constant rate of 1616 of the length of circular path per hour.

n/1818 = m/1616
n/9 = m/8

Since 9 and 8 are co-prime, the two places would be together when Ship makes 9 circular paths and Car makes 8 circular paths. Thus, they together make 8 +9 = 17 circular paths when for the first time after 5 pm, the two planes would be at the same location above Town X.

The correct answer: B

Hope this helps!

-Jay
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