A boat can go 3 km upstream and 5 km downstream in 55 minutes. It can also go 4 km upstream and 9 km downstream in 1 hour 25 minutes. In how much time(in hours) will it go 43.2 km downstream?

Let the speed of stream be u and speed of boat be v.

Speed in upstream = v - u

Speed in downstream = v + u

A boat can go 3 km upstream and 5 km downstream in 55 minutes so,

$$\frac{3}{v - u} + \frac{5}{v + u} = \frac{55}{60}$$

Boat can go 4 km upstream and 9 km downstream in 1 hour 25 minutes

$$\frac{4}{v - u} + \frac{9}{v + u} = 1 + \frac{25}{60}$$

$$\frac{4}{v - u} + \frac{9}{v + u} =  \frac{85}{60}$$

$$\frac{1}{v - u}$$ = x

$$\frac{1}{v + u}$$ = Y

$$3x +5y = \frac{11}{12}$$ ---(1)

$$4x +9y = \frac{17}{12}$$ ---(2)

eq(1) multiply by 4 and eq(2) multiply by 3,

$$12x +20y = \frac{44}{12}$$ ---(3)

$$12x +27y = \frac{51}{12}$$ ---(4)

From eq (3) and (4),

7y = $$\frac{7}{12}$$

y = $$\frac{1}{12}$$

From eq(1),

$$3x +5 \times \frac{1}{12} = \frac{11}{12}$$

$$3x  = \frac{6}{12}$$

$$x = \frac{1}{6}$$

$$\frac{1}{v - u} =  \frac{1}{6}$$

v - u = 6 ---(5)

$$\frac{1}{v + u} = \frac{1}{12}$$

v + u = 12 ---(6)
Speed in downstream = u + v = 12 km/hr

Time taken by boat = 43.6/12 = 3.63 hr