A boat covers 16 km upstream and 24 km downstream in 4 hours, while it covers 24 km upstream and 16 km downstream in 4\(\frac{1}{2}\). The speed of current is?

3.03 km/hr

Let the speed of boat = U km/hr

Speed of stream = V km/hr

ATQ,      \(\frac{24}{U + V}\) + \(\frac{16}{U-V}\) = 4 hours ------- (i)

             \(\frac{16}{U+V}\)   +  \(\frac{24}{U-V}\) = 4\(\frac{1}{2}\)  hours -------- (ii)

Solving,

mutiplying eq. (i) by 2 and eq. (ii) by 3,

       \(\frac{48}{U + V}\) + \(\frac{32}{U-V}\) = 8 hours ------- (iii)

      \(\frac{48}{U + V}\) + \(\frac{72}{U-V}\) =  \(\frac{27}{2}\)  hourshours ------- (iv)

Subtracting, eq. (iii) from eq. (iv)

                       0                +   \(\frac{40}{U-V}\) = 5\(\frac{1}{2}\) hours

So, U - V = 7\(\frac{3}{11}\)   

After putting value of U - V in equation (i)

                               \(\frac{24}{U+V}\) + \(\frac{16}{7\frac{3}{11}}\) = 4 hours

                                                  U + V   =  13\(\frac{1}{3}\)

Then speed of current (V) =  \(\frac{13\frac{1}{3} - 7\frac{3}{11}}{2}\) = 3.03 km/hr