A boat covers 150 km downstream and 40 km upstream in 4 hours while it covers 70 km downstream and 24 km upstream in 2 hours. Determine the velocity of the current?

5 km/hr

The correct answer is Option (3) → 5 km/hr

Let the speed of the boat in still water = b km/h
Let the speed of the current = c km/h

So,

• Downstream speed = b + c
• Upstream speed = b - c

Given equations:

1. $\frac{150}{b+c} + \frac{40}{b-c} = 4$
2. $\frac{70}{b+c} + \frac{24}{b-c} = 2$

Multiply equation (2) by 2:

$\frac{140}{b+c} + \frac{48}{b-c} = 4$

Now subtract equation (1) from this:

$\left(\frac{140}{b+c} - \frac{150}{b+c}\right) + \left(\frac{48}{b-c} - \frac{40}{b-c}\right) = 0$

$\frac{-10}{b+c} + \frac{8}{b-c} = 0$

$\frac{8}{b-c} = \frac{10}{b+c}$

$8(b+c) = 10(b-c)$

$8b + 8c = 10b - 10c$

$18c = 2b \Rightarrow b = 9c$

Substitute into equation (2):

$\frac{70}{10c} + \frac{24}{8c} = 2$

$\frac{7}{c} + \frac{3}{c} = 2$

$\frac{10}{c} = 2 \Rightarrow c = 5$

Velocity of the current = 5 km/hr