A motor boat can travel 30 km upstream

Asked by admin @ in Math viewed by 351 People

A motor boat can travel 30km upstream and 28 km downstream in 7 hours. it can travel 21 km upstream and return in 5 hours. find the speed of boat in still water and speed of the stream.

Answered by admin @


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

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