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?
Answer & explanation
Correct answer: option 1
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