Question

Please Solve this Question No.13​

Answer 1

$\Large{ \underline{\underline{ \bf{Question:}}}}$

The speed of a boat downstream in 12 km/hr and it's speed upstream is 6 km/hr. Find the speed of the boat in still water and speed of the stream.

$\Large{ \underline{\underline{ \bf{Required \: answer:}}}}$

GiveN:

• Speed downstream = 12 km/hr
• Speed upstream = 6 km/hr.

Let the speed of the boat in still water be x and the speed of the stream be y. By using the concept of relative motion,

• x + y = 12 km/hr
• x - y = 6 km/hr

Adding eq. (1) and eq.(2),

➛ x + y + x - y = 18 km/hr

➛ 2x = 18 km/hr

➛ x = 9 km/hr

Then, y = 12 km/hr - 9 km/hr

➛ y = 3 km/hr

Hence,

• Speed of the boat in still water is 9 km/hr and speed of the stream is 3 km/hr.

Shortcut method:

You can also use the shortcut method of finding the speed of boat in still water and speed of stream.

Let the speed downstream be a km/hr and the speed upstream be b km/hr, then

• Speed of boat = 1/2 (a + b) km/hr
• Speed of stream = 1/2 (a - b) km/hr

Answer 2

The speed of the boat downstream = 12 km/hr

The speed of the boat upstream = 6 km/hr

Let , the speed of boat in still water be x

and the speed of stream be y

So ,

The speed of the boat downstream is (x + y) i.e

x + y = 12 ------ (i) {given}

The speed of the boat upstream is (x - y) i.e

x - y = 6 ------ (ii) {given}

Add equation (i) and (ii) , we get

2x = 18

x = 9

Put the value of x = 9 in eq (i) , we get

9 + y = 12

y = 3

Hence , the speed of boat in still water and the speed of the stream are 9 km/hr and 3 km/hr

________________

let X be the speed of the stream

speed of the boat in still water = to 8 km /hr

thus the speed of the boat in upstream =(8-x) km/hr

speed of the boat in downstream =(8+x )km/hr

Time = distance/speed

the time taken by boat to cover 15 km=15/8-x

the time taken by boat to cover 22 km=22/8+x

$\begin{array}{l}\frac{15}{8-x}+\frac{22}{8+x}=5 \\15(8+x)+22(8-x)=5(8-x)(8+x) \\120+15 x+176-22 x=5\left(64-x^{2}\right) \\296-7 x=320-5 x^{2} \\5 x^{2}-7 x-24=0 \\5 x(x-3)+8(x-3)=0 \\(5 x+8)(x-3)=0 \\5 x+8=0 \text { or } x-3=0 \\x=\frac{-8}{5}=0 \text { or } x=3\end{array}$

total time =5hrs (given)

x=3

since speed cannot be negative

Therefore speed of steam is 3km/hr