Question

If a motorboat 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 speed of the stream

Answer 1

please refer to the pics..

Answer 2

Speed of the boat is 10 km/hr

Speed of the stream is 4 km/hr

Given:

In 7 hours, boat can travel 30 km and 28 km, upstream and downstream respectively.

Step-by-step explanation:

Let the boat’s speed be x and the stream’s speed be y.

Using the speed, distance and time relation we have:

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

Let,

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

And

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

30a + 28b = 7 → (1)

We are also given that the boat can travel 21 km upstream and return in 5 hours.

$\frac{21}{x-y}+\frac{21}{x+y}=5$

Using the relations mentioned above we have:

21a + 21b = 5 → (2)

Solving (1) & (2), we get:

42a = 7

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

Substituting a in (1), we get,

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

Rearranging the constituents we get the value of b as:

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

We know that,  

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

x - y = 6 → (3)

We know that,

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

x + y = 14 → (4)

On solving (3) & (4), we get,

x = 10

y = 4