Question

A motor boat goes down the stream 30 km and agam
retums 10
starting point in a total time of 4 hours and 30 minutes.
stream is 5 km/hr, then find the speed of the motor boat in su​

Answer 1

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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 is the speed of the boat in still water

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