Question

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. Find the speed of the boat in still water and the speed off the stream.

Answer 1

Answer:

The speed of the boat in still water = 10 km/hr and the speed of the stream = 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 the boat in still water and the speed off the stream?

Solution :

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

Let the speed of the stream = y km/hr.

Speed upstream = x - y

Speed Downstream = x + y

Now,

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

i.e, $\frac{30}{x-y}+\frac{28}{x+y}=7$

Let, $\frac{1}{x-y}=a$ and $\frac{1}{x+y}=b$

Then, $30a+28b=7$  ---------------------------- (1)

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

Also, Given that it can travel 21 km upstream and return in 5 hours.

i.e, $\frac{21}{x-y}+\frac{21}{x+y}=5$

Let, $\frac{1}{x-y}=a$ and $\frac{1}{x+y}=b$

Then, $21a+21b=5$  ---------------------------- (2)

Solving (1) and (2)

Multiply (1) by 21 and (2) by 28

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

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

Solving (3) and (4)

$42a=7$

$a=\frac{1}{6}$

Substitute a in (1), we get

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

$5+28b=7$

$28b=2$

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

We know that, 

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

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

i.e, $x-y=6$ -----------(5)

and $\frac{1}{x+y}=b$

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

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

Solving equation (5) and (6)

Add equation (5) and (6)

$2x=20\\x=10$

Substitute in (5)

$10-y=6\\y=4$

Therefore, The speed of the boat in still water = 10 km/hr and the speed of the stream = 4 km/hr.