Question

a Boat covers 32 km upstream and 36 km downstream in 7 hour also it car cover 40 kilometre upstream and 48 km downstream in 9 Hour find the speed of the boat​

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Answer 1

Always keep in ur mind,

Speed of boat (B) > Speed of stream (S)

In upstream, B-S

In downstream, B+S

Let the speed of boat in still water be x km/h and speed of stream be y km/h

Therefore, speed of boat in upstream = (x-y) km/h and speed of boat in downstream = (x+y) km/h

According to question, the equation stands like this :

32/(x-y) + 36/(x+y) = 7....... (i)

Similarly, 40/(x-y) + 48/(x+y) = 9........ (ii)

Now, let 1/(x-y) = u and 1/(x+y) = v

Then for first and second equations,

32u + 36v = 7......... (iii)

40u + 48v = 9......... (iv)

Multiplying equation (iii) and (iv) by 10 and 8 respectively, we get :

320u + 360v = 70

320u + 384v = 72

From the above two obtained equations, by calculation, we get that v = 1/12 and u = 1/8

Now, 1/x-y = 1/8

Or, x-y = 8

Also, 1/x+y = 1/12

Or, x+y = 12

Hence, clearly x = 10km/h and y=2km/h

Thus, speed of boat in still water is 10 km/h.