Question

can anyone please answer this question ​

Answer 1

Given :---

• speed of motor boat in still water = 9km/h
• Total time taken for 15 km downstream and coming back = 3 hours 45 min .

To Find :---

• Speed of stream = ?

Concept used :---

• when going downstream , speed becomes = speed of boat + speed of stream .
• while coming upstream , speed = speed of boat - speed of stream .
• 60 min = 1 hour .
• Time = Distance / Speed .

Solution :---

Let speed of stream is x km/h .

Than,

→ Speed in downstream = (9+x) km/h .

→ Speed in upstream = (9-x) km/h .

Now, he goes 15 km downstream and come back same 15km upstream in 3 hours 45 min ,

→ 3 hours 45 min = 3 ( 45/60) = 3(3/4) = 15/4 hours .

_____________________________

According to Question now,

→ 15/(9+x) + 15/(9-x) = 15/4

→ 15(1/9+x + 15/9-x ) = 15/4

( 15 cancel from both sides )

→ 1/(9+x) + 1/(9-x) = 1/4

Taking LCM now,

→ (9-x + 9+x)/[(9-x)(9+x)] = 1/4

→ 18/(81 - x² ) = 1/4 [ using (a+b)(a-b) = a² - b² ]

Cross - Multiply now,

→ 81 - x² = 72

→ x² = 81 - 72

→ x² = 9

→ x² = 3*3

→ x = 3 km/h

Hence, speed of stream is 3km/h ..

Answer 2

Answer:

3 km/hr

Step-by-step explanation:

Let the speed of stream be x km/h

Given,

Speed of boat is 9 km/hr

Speed downstream = (9 + x) km/h

Speed upstream = (9 - x) km/h

Distance covered = 15 km

Time taken = 3 hours 45 minutes = (15/4) hours.

Now,

(15/9 + x) + (15/9 - x) = 15/4

⇒ (1/9 + x) + (1/9 - x) = 1/4

⇒ (9 - x + 9 + x)/(9 + x)(9 - x) = 1/4

⇒ 18/(9 + x)(9 - x) = 1/4

⇒ 18/9² - x² = 1/4

⇒ 18/81 - x² = 1/4

⇒ 72 = 81 - x²

⇒ x² = 81 - 72

⇒ x² = 9

⇒ x = 3, -3 {Speed cannot be negative}

⇒ x = 3

Therefore,

Speed of the stream is 3 km/hr.

Hope it helps!