Question

a motorboat can travel 30 km upstream and 28 km downstream by 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​

Answer 1

This kind of questions follows the same pattern:

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.

NOTE: Sorry, for making such a lengthy calculations.

Hope this helps! --------------- Gud Luck