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In ChudoGrad City police stations are located in such a way that the police can

ID: 1561780 • Letter: I

Question

In ChudoGrad City police stations are located in such a way that the police can reach any crime scene within 4 minutes. Fire stations are located in such a way that the fire trucks can reach any place in 6 minutes 30 seconds. Assume that the velocities of police cars and fire trucks are the same and the neighborhoods of responsibility for both of them are geometrically similar. Estimate the minimal number of police stations, if it is given that there are 53 fire stations in this city. A long time ago in a galaxy far, far away. In order to control the galaxy, The Empire's spaceships need to be able to reach any point in the galaxy within 24 hours. There are two types of spaceships available: space cruisers (speed 0.1 astronomical units per hour; building price 1,000 credits) and more advanced battleships (speed 0.4 astronomical units per hour; building price 50,000 credits). The whole galaxy can be taken under control with 6400 space cruisers. How many battleships are needed in order to do this?

Explanation / Answer

No. stations is inversely proportional to the time taken to reach the scene.

More the no. of stations , time taken to reach the scene minimal.

Let x1 = No. of police stations and x2 = No.of fire stations

y1 =Time taken by police cars to reach crime scene. and y2 =Time taken by fire trucks to reach any place  

x1 = ? ;  x2 = 53 ; y1 = 4*60 = 240 seconds ; y2 = 6*60 +30 =390 seconds

As these two quantities are in inverse proportion

x1 / x2 =y2 / y1

x1 = (390 / 240) * 53 = 86.1 = 86

So. the minimal No. of police stations = 86 ANS