Question

7. 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.
[CBSE 2012)​

Answer 1

Answer  

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,

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.

NOTE: Sorry, for making such a lengthy calculations.