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. If the speed of the
stream is 5 km/hr, then find the speed of the motor boat in still water.​

Answer 1

Answer:

Let the speed of the stream be x km/hr. Then,

Speed downstream = (15 + x) km/hr,

Speed upstream = (15 - x) km/hr.

30 + 30 = 4 1

(15 + x) (15 - x) 2

900 = 9

225 - x2 2

9x2 = 225

x2 = 25

x = 5 km/hr

Plz mark brainliest ❤️❤️❤️❤️❤️❤️

Step-by-step explanation:

Answer 2

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