Question

There are n missiles placed at the starting point of a track and are fired one by one..The speed of each missile is equal to twice the sum of speeds of all the preceding missiles.If the 10th missile covers the track in 5min,then find the time taken by 8th missile (in min,)to cover the track

Answer 1

Answer:

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Answer 2

The time taken by 8th missile to cover the track is 45minutes.

Given:-

Number of missiles = n

Speed of each missile = 2(sum of speed of all preceding missiles)

Time taken by 10th missile to cover track = 5min

To Find:-

The time taken by 8th missile to cover the track.

Solution:-

We can easily calculate the value of time taken by 8th missile to cover the track by using these simple steps.

As

Number of missiles = n

Speed of each missile = 2(sum of speed of all preceding missiles)

Time taken by 10th missile to cover track = 5min

So, if the speed of first missile = v

then,

speed of second missile = 2v

speed of third missile = 2(2v+v) = 6v

speed of fourth missile = 2(6v+2v+v) = 18v

speed of fifth missile = 54v

speed of sixth missile = 162v

speed of seventh missile = 486v

speed of eighth missile = 1458v

speed of ninth missile = 4374v

speed of tenth missile = 13122v

Also, let the distance covered be x

So, According to the formula

$speed = \frac{distance}{time}$

$time = \frac{distance}{speed}$

for 10th missile,

$t10 = \frac{x}{13122v}$

$5 = \frac{x}{ 13122v}$

$x = 5 \times 13122v$

$x = 65610v$

Now, for 8th missile,

$t8 = \frac{x}{1458v}$

$t8 = \frac{65610v}{1458v}$

$t8 = \frac{65610}{1458}$

$t8 = 45min$

Hence, The time taken by 8th missile to cover the track is 45minutes.

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