A Motor boat goes downstream 30 km and again returns to the starting point in a total time of 4 hours and 30 minutes if the speed of the stream is 5 kilometre per hour then find the speed of motor boat in still water.

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

Step-by-step EXPLANATION:

The speed of the boat in still water is 15 km/hr.

Total time taken by the motorboat = 4 hrs 30 minutes = 4 ½ hr = (9/2) hrs

The distance TRAVELLED by boat during downstream = 30 km

The speed of the stream = 5 km/hr

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

So,

The speed of the boat downstream = (x + 5) km/hr

The speed of the boat upstream = (x - 5) km/hr

and,

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

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

Therefore, according to the question, we can write the eq. as,

[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

Neglecting the negative value

⇒ x = 15 km/hr ← speed of the boat in still water

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