Question

A rescue boat takes 12 hours to row 90 km downstream and 70 km upstream. what is the rate of current if the boat takes 9 hours to row 72 km downstream?

Answer 1

Let the speed of boat is B
and the speed of current is C
now, speed of downstream = (B + C) Km/h
speed of upstream = (B - C) Km/h

we know,
time = distance /speed
so, time taken in downstream + time taken in upstream = 12 h
90/(B + C) + 70/(B - C) = 12 ----(1)

time taken in downstream = 9 h
72/(B + C) = 9
B + C = 8 km/h---------(2) , put it in equation (1)

90/8 + 70/(B -C) = 12
45/4 + 70/(B - C) = 12
70/(B - C) = 12 - 45/4 = 3/4
B - C = 280/3 km/h -------(3)

solve both equations (2) and (3),
2B = 280/3 + 8 => B = 140/3 + 4 = 152/3 km/h

now, Put B in equation (2) ,
C = 8 - 152/3 = (24-152)/3 = -128/3 km/h

here , negative sign shows that Current is just opposite side of our assumption .
hence, speed of current = -128/3 km/h

Answer 2

Let Speed of Boat be B 
and  Let Seed of Water be A
 Thus

While Going Upstream

Speed = A - B
and
While going downstream
Speed = A + B

Thus

Since   Speed = Distance / Time
So    Time  = Distance / Speed
While Going Upstream

Time   t = 70 / A - B
           12 = 70 / A - B
A - B = 70/12        Eqn 1

Similarly While going downstream

12 = 90 / A + B
A + B = 90 / 12         Eqm 2

Solving Eqn 1 and 2
2A = 160 / 12
A = 80 / 12
A = 6.66 Km /Hr
Thus B = 7.5 - 6.66
        B = 0.9 Km /hr