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
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
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.