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A motor boat can travel 30 km upstream and 28 km downstream in 7 hrs it can travel 21km upstream and return in 5 hrs find the speed of the boat in still water and the speed of the stream.?
Most Upvoted Answer
A motor boat can travel 30 km upstream and 28 km downstream in 7 hrs i...
Let the speed of the boat in still water = xkm/hr.

Let the speed of the stream = ykm/hr.

Speed upstream = x - y.

Speed Downstream = x + y.


Now,

Given that boat can travel 30km upstream and 28km downstream in 7 hours.

30/x-y + 28/x+y = 7 

Let 1/x - y = a and 1/x + y = b

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

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

21/x - y + 21/x + y = 5

Let 1/x - y = a and 1/x + y = b 

21a + 21b = 5   ------------------------ (2)


On solving (1) * 21 & (2) * 28, we get

630a + 588b = 147

588a + 588b = 140
-----------------------------
42a = 7

a = 1/6.

Substitute a = 6 in (1), we get

30a + 28b = 7

30(1/6) + 28b = 7

5 + 28b = 7

28b = 7 - 5

28b =2

b = 2/28

b = 1/14.

We know that, 

a = 1/x - y

1/6 = 1/x - y

x - y = 6   ----------- (3)


We know that,

b = 1/x + y

1/14 = 1/x + y

x + y = 14   ------------ (4).


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

x + y = 14

x - y = 6

------------

2x = 20

x = 10


Substitute x = 10 in (4), we get

x + y = 14

10 + y = 14

y = 14 - 10

y = 4.


Therefore the speed of the boat in still water = 10km/hr.

Therefore the speed of the stream = 4km/hr.
Community Answer
A motor boat can travel 30 km upstream and 28 km downstream in 7 hrs i...
Given:

Distance travelled upstream = 30 km

Distance travelled downstream = 28 km

Time taken for upstream and downstream journey = 7 hours

Distance travelled upstream and return = 21 km

Time taken for upstream and return journey = 5 hours

We need to find the speed of the boat in still water and the speed of the stream.

Let:

Speed of boat in still water = b km/hr

Speed of stream = s km/hr

Speed of boat upstream = (b - s) km/hr

Speed of boat downstream = (b + s) km/hr

Calculating speed of boat in still water:

Let's first consider the upstream and downstream journey of 30 km and 28 km respectively.

Using the formula: Time = Distance/Speed

Time taken to travel upstream = 30/(b-s)

Time taken to travel downstream = 28/(b+s)

As per the given information, the total time taken for upstream and downstream journey is 7 hrs.

Therefore, we can form the equation:

30/(b-s) + 28/(b+s) = 7

Simplifying the equation, we get:

15b/bs = 7

Similarly, for the upstream and return journey of 21 km, we can form the equation:

21/(b-s) + 21/(b+s) = 5

Simplifying the equation, we get:

21b/bs = 5

Dividing the above two equations, we get:

15/7 = b/2b

Therefore, b = 10.5 km/hr

Calculating speed of stream:

Using the formula: Time = Distance/Speed

For the upstream and downstream journey of 30 km and 28 km respectively, we can form the equation:

30/(10.5-s) + 28/(10.5+s) = 7

Simplifying the equation, we get:

s = 1.5 km/hr

Conclusion:

The speed of the boat in still water is 10.5 km/hr and the speed of the stream is 1.5 km/hr.
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A motor boat can travel 30 km upstream and 28 km downstream in 7 hrs it can travel 21km upstream and return in 5 hrs find the speed of the boat in still water and the speed of the stream.?
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