Question

A motor-boat, whose speed is 9 km/h in still water goes 12 km downstream and comes back in a total time of 3 hours. Find the speed of the stream.​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Information given to us:

• Speed of motor-boat = 9km/h
• In still water its speed goes upto 12km downstream
• Total time taken is 3 hours

What we have to calculate:

• Speed of stream?

Let us assume:

• Speed of stream be y km/hr

Speed of motor-boat in downstream:

As we have assumed speed as y km/hr. So speed of motor-boat in downstream would be found out by adding the speed of boat in still water with assumed speed.

• → (9 + y) km/hr

Speed of motor-boat in upstream:

As we have assumed speed as y km/hr. So speed of motor-boat in upstream would be found out by subtracting the speed of boat in still water with assumed speed.

• → (9 - y) km/hr

Formula needed to be used:

• T = D /S

Where,

• T denotes time
• D denotes distance
• S denotes speed

Finding out time taken for going 12 km downstream:

Again given,

• Distance = 12 km
• Speed = (9+x) km/hr

Applying the given formula of time.

• → (12 / 9+y) hr _______(1)

Finding out time taken for coming back from downstream:

Again given,

• Distance = 12km
• Speed = (9-x) km/hr

Applying the given formula of time:

• → (12 / 9-y) hr _______(2)

Adding both the equations which would be equal to 3 hours:

• → (12/9+y) + (12/9-x) = 3

Talking L.CM.,

• → (108 + 108 - 12y + 12y) / (9+y)(9-y) = 3

Opening the brackets in denominator and solving

• (9+y) (9-y)
• 9 (9-y) + y (9-y)
• 81 - 9y + 9y - y²
• 81 - y²

Again solving the equation,

• → (108 + 108 - 12y + 12y) / (81 - y²) = 3
• → (216) / (81 - y²) = 3

On cross multiplying we get,

• → 3 (81 - y²) = 216

Dividing 216 with 3,

• (81 - y²) = 216/3

Now,

• (81 - y²) = 72

Reversing the sides,

• -y² = 72 - 81
• -y² = -9

Negative signs would be cancelled,

• y² = 9

Taking square,

• y = √9

We gets, at last

• y = 3

Conclusion:

• Speed of the stream. is 3 km/hr