Question

A motor boat takes 6 hours to cover 100 km downstream and 30 km upstreet , if the boat goes 75 km downstream and returns back to the starting point in 8 hours , find the speed of the boat in still water and speed of the stream..???

Answer 1

Let the speed of boat is still water = x km/hr
Let the speed of stream = y km/hr

Thus speed of boat whie going downstream is (x + y)km/hr
speed of boat whie going upstream is (x - y)km/hr

Distance = speed x time
time = Distance/speed

As per question, equations are

6 = 100/(x + y) + 30/( x - y) 
3 = 50/(x + y) + 15/( x - y) -------- (1)
8 = 75/(x + y) + 75/( x - y) -------- (2)

Let 1/(x + y) = p; 1/(x - y) = q

the resultant equations are

3 = 50p + 15q -------- (3)
8 = 75p + 75q -------- (4)

On multiplying eq (3) by 5 we get
15 = 250p + 75q -------- (5)

On subtracting eq (4) from (5) we get
175p = 7
p = 7/175 = 1/25 

On putting value of "p" in eq. (3), we get

3 = 50(1/25) + 15q 
3 = 2 + 15q
15q = 1
q = 1/15 

Thus p = 1/(x+y)                                         q = 1/(x - y)
1/25 = 1/(x+y)                                             1/15 = 1/(x - y)               
x+y = 25   ------ (6)                                     x - y = 15 ----- (7)

On adding eq. (6) and (7), we get
2x = 40
x = 20 Ans

Put value of "x" in eq (6), we get

20 + y = 25
y = 5 Answer

Answer 2

The answer is in the pics below

I hope this helps you out

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