Question

the speed of a sparrow is x km/ h in still air. when the wind is blowing at 1 km/ hour, the sparrow takes 5 hours to fly 12 km to her nest and 12 km back again. she goes out directly into the wind and returns with the wind behind her. find her speed in still air

Answer 1

When sparrow flies into the wind, its speed is (x-1) km/h.
When is flies in the direction of the wind, its speed is (x+1) km/h.

Therefore time taken to fly to the nest = Distance/speed = 12 /(x-1).
Also time taken to fly back = 12 / (x+1).
Total time taken = 5 hrs.

Therefore [12/(x-1)] + [12/(x+1)] = 5

On simplifying, this reduces to 5x² - 24x - 5 = 0
                                             5x² - 25x + x - 5 = 0
                                             5x(x-5) + (x - 5) = 0
                                             (x - 5)(5x + 1) = 0
Hence speed of sparrow in still air = 5.

Answer 2

The speed of the sparrow in still air is 5 km/h.

Given: The speed of a sparrow is x km/ h in still air. when the wind is blowing at 1 km/ hour, the sparrow takes 5 hours to fly 12 km to her nest and 12 km back again.

To Find: The speed of the sparrow in still air.

Solution:

It is said that the speed of a sparrow is x km/ h in still air.

Let us assume that the sparrow will fly against the direction of the wind when it travels towards its nest. So, we can say that;

The speed of the sparrow while traveling to its nest is = ( x - 1 ) km/h.

The speed of the sparrow traveling back from its nest is = ( x + 1 ) km/h.

The distance of the sparrow from its current location and the nest= 12 km

So, the time is taken to fly to the nest = Distance/speed

                                                           = 12 / ( x - 1 ) hrs

The time taken to fly back from the nest = 12 / ( x + 1 )  hrs

It is also said that the total time taken for the sparrow to go to its nest and come back is 5 hrs.

So, the total time traveled = 5 hrs

Now, from the above information, we can frame an equation;

                     [ 12 / ( x - 1 )] + [ 12 / ( x + 1 )] = 5

                ⇒  12 [( x + 1 + x - 1 ) / ( x - 1 )×( x + 1 )] = 5

                ⇒  12 [ 2x / ( x² - 1 )] = 5

                ⇒  24x = 5x² - 5

                ⇒  5x² - 24x - 5 = 0

                ⇒  5x² - 25x + x - 5 = 0

                ⇒  5x ( x - 5 ) + 1 ( x - 5 ) = 0

                ⇒  ( x - 5 ) ( 5x + 1 ) = 0

So, the value of x = 5, - 1/5

Since the speed cannot be negative so we shall omit - 1/5.

Hence, the speed of the sparrow in still air is 5 km/h.

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