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 of the stream.

# 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 of the stream.

1. A
speed of boat = 6km/h and speed of stream = 10km/h
2. B
speed of boat = 5km/h and speed of stream = 2km/h
3. C
speed of boat = 2km/h and speed of stream = 5km/h
4. D
speed of boat = 10km/h and speed of stream = 4km/h

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### Solution:

Given that a motor boat can travel 30 km upstream and 28 km downstream in 7 hours and it can travel 21 km upstream and return in 5 hours. We need to find the speed of the boat in still water and the speed of the stream.
A system of linear equations   and  , cross multiplication method is given as:

We will form a pair of linear equations and solve them by using cross-multiplication method.
Let speed of boat in still water be x km/h and speed of stream be y km/h.
Time taken to cover 30 km upstream is  .
Time taken to cover 28 km downstream is  .
Time taken to cover 21 km upstream is  .
Time taken to cover 21 km downstream is  .
According to the question, we have,

Let us assume   and  , then we have,

Now solving these equations by cross multiplication we have,

On comparing we have,

Similarly, we have,

From here we have,

Now, adding equation (i) and (ii), we have,

Now substituting the value of x in equation (ii), we have,

Hence the speed of stream and that of the boat in still water are 4 km/h and 10 km/h respectively.
Therefore, option 1 is correct.

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