Question

A motor boat goes down the stream 30 km and again returns to the
starting point in a total time of 4 hours and 30 minutes. Ir the speed of the
stream is 5 km/hr, then find the speed of the motor boat insult water
​

Answer 1

Given :-

• A motor boat goes down the stream 30 km and again returns to the starting point in a total time of 4 hours and 30 minutes.
• The speed of the stream is 5 km/hr.

To Find :-

• Find the speed of the motor boat in still water.

Solution :-

So, Let we consider the speed of the boat in still water be “x” km/hr.

From given we know :-

• The speed of the boat downstream = (x + 5) km/hr
• The speed of the boat upstream = (x - 5) km/hr$.$

Therefore,

• Time taken to travel downstream = 30/(x+5)
• Time taken taken to travel upstream = 30/(x-5)

Now let's make an equation :-

⇒ [ 30 /(x + 5) ] + [ 30 / (x - 5) ] = 9/2

⇒ 30 [ (x - 5 + x + 5) /{(x - 5)( x + 5) }] = 9/2

⇒ 30 [( 2x ) / ( x² - 25 )] = 9/2

⇒ 10 [( 2x) / ( x² - 25 )] = 3/2

⇒ 40x = 3x² – 75

⇒ 3x² – 40x – 75 = 0

⇒ 3x² – 45x + 5x – 75 = 0

⇒ 3x ( x - 15 ) + 5( x - 15 ) = 0

⇒ (x - 15 )( 3x + 5 ) = 0

⇒ x = 15 or -5/3

As we know that negative value can't considered.

So,

Speed of motor boat in still water is 15 km/h.

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