Question

A boat goes 12 km upstream in 48 minutes. The speed of stream is 2 km/hr. The speed of boat in still water is ?​

Answer 1

the speed of boat in still water is 17 km/h

upstream means opposite direction from that stream flows .

if v is speed of boat in still current and y is the speed of stream.

then upstream, speed of boat = (v - y) km/h.

here given, speed of stream = 2km/h

so, speed of boat will be (v - 2)km/h

and time taken = 48 min = 48/60 = 4/5 hr

distance travelled = 12km

we know, speed = distance/time

⇒(v - 2) km/h= 12km/(4/5 h) = 15 km/h

⇒v = 15 + 2 = 17 km/h

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Answer 2

Given: A boat goes $12$ km upstream in $48$ minutes and speed of stream is $2$ km/hr.

To Find: What is the speed of boat in still water.

Step-by-step explanation:

Let,

The speed of the boat in still water $=x$ km/hr.

The average speed of the current $=2$ km/hr.

Therefore,

The speed of the boat upstream$=(x-2)$ km/hr and the speed of the boat down stream$=(x+2)$ km/hr.

Distance traveled upstream$=12$ km.

It takes $48$ minutes$=0.8$ hr. longer to move in upstream.

Therefore,

                 $\frac{12}{x-2}=\frac{12}{x+2}+0.8$

           ⇒$\frac{12}{x-2}-\frac{12}{x+2}=0.8$

           ⇒ $\frac{12(x+2)-12(x-2)}{x^{2}-4}=0.8$

           ⇒$12x+24-12x+24=0.8x^{2}-3.2$

           ⇒$0.8x^{2}=48+3.2$

           ⇒$x^{2}=\frac{51.2}{0.8}$

           ⇒$x^{2}=64$

           ∴ $x=8$

So, The speed of the boat in still water is $8$ km/hr.