A motor boat can travel 30 km upstream and 28 km downstream in 7 hours. It can also travel 21 km upstream and return in 5 hours. Calculate the speed of the boat when it is in still water in km/h

A motor boat can travel 30 km upstream and 28 km downstream in 7 hours. It can also travel 21 km upstream and return in 5 hours. Calculate the speed of the boat when it is in still water in km/h

  1. 3
  2. 15
  3. 10
  4. 11

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Solution:

Let the speed of the boat when it is in still water be x km/h.

Then the speed of the stream is y km/h.

The speed of the boat when it is upstream is (x-y) km/h

The speed of the boat when it is downstream is (x+y) km/h

Speed = distance/time

Time = distance/speed

From the question we know that the boat travels 20 km upstream and 28 km downstream in 7 hours, and it can also travel 21 km upstream and return in 5 hours

(30/x+y) + (28/x-y) = 7 eq.1

(21/x+y) + (21/x-y) = 5 eq.2

Let (1/x+y) and (1/x-y) be u and v respectively in the eq.1 and eq.2

Therefore,

30u + 28V = 7 eq.3

21u + 21v = 5 eq.4

Multiplying the eq.3 by 21 and eq.4 by 30

630u + 588v = 147 eq.5

630u + 630v = 150 eq.6

Subtracting the above equations, we get

v = 1/14

When v is substituted in eq.4, we get u = 1/6

Substituting u and v in (1/x+y) and (1/x-y), we get,

x+y = 6 eq.7

x-y = 14 eq.8

Adding eq.7 and eq.8,

x = 10.

Therefore, option iii. 10 is the value of the speed of the boat in still water.

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