Question

A motor boat can travel 30km upstream and 28 km downstream in 7 hours. it can travel 21 km upstream and return in 5 hours. find the speed of boat in still water and speed of the stream.

Answer 1

downstream is not given in Second case

Answer 2

Answer:

The speed of the boat in still water is 10 km/hr.

The speed of the stream is 4 km/hr.                

Step-by-step explanation:

Given : A motor boat can travel 30 km upstream and 28 km downstream in 7 hours. it can travel 21 km upstream and return in 5 hours.

To find : The speed of boat in still water and speed of the stream?

Solution :

Let the speed of the boat in still water be 'x' km/hr.

The speed of the stream is 'y' km/hr.

Upstream speed is 'x-y'

Downstream speed is 'x+y.

According to question,

A motor boat can travel 30 km upstream and 28 km downstream in 7 hours.

Time taken is  $\frac{30}{x-y}+\frac{28}{x+y}=7$

It can travel 21 km upstream and return in 5 hours.

Time taken is $\frac{21}{x-y}+\frac{21}{x+y}=7$

Now, Substitute $a=\frac{1}{x-y}, b=\frac{1}{x+y}$ .......(A)

$30a+28b=7$ .....(1)

$21a + 21b = 5$ .....(2)

Solving equation (1) and (2) by multiplying (1) with 21 and (2) with 28,

$630a + 588b = 147$ ....(3)

$588a + 588b = 140$ ....(4)

Subtract (3) and (4),

$630a + 588b-588a-588b= 147-140$

$42a=7$

 $a=\frac{7}{42}$

 $a=\frac{1}{6}$

Substitute in (1),

$30a+28b=7$

$30(\frac{1}{6})+28b=7$

$5+28b=7$

$28b=2$

$b=\frac{2}{28}$

$b=\frac{1}{14}$

Substitute the value of a and b in (A),

$\frac{1}{6}=\frac{1}{x-y}$

$x-y=6$ .....(5)

$\frac{1}{14}=\frac{1}{x+y}$

$x+y=14$ ....(6)

Solving equation (5) and (6) by adding them,

$x-y+x+y=6+14$

$2x=20$

$x=10$

Substitute in (5),

$10-y=6$

$y=4$

Therefore, The speed of the boat in still water is 10 km/hr.

The speed of the stream is 4 km/hr.