Question

A boatman can row 2 km against the stream in 20 minutes and return in 10
minutes. Find the rate of flow of the current.​

Answer 1

Answer:

3km/hr

Explanation:

Let x be the speed of man in still water and y be the speed of the

current.

Speed of d / s = (2 / 10) × 60 = 12 km / hr. Speed of u / s = (2 / 20) × 60 = 6 km / hr.

∴ rate of current = (12 - 6) / 2 = 3 km/hr.

Answer 2

Given,

Distance covered by the boatman = $2Km$

Time taken for upstream = $20 min$

Time taken for downstream = $10min$

Now,

Relative velocity of the boatman w.r.t to water

$V_{wb}=\frac{total\_distance}{time\_ taken}$

let velocity of boat = $V_b$

velocity of water = $V_w$

Now, there will be two different relative velocities for upstream and downstream.

1) Upstream relative velocity: here the velocity of water decrease the velocity of boat. Therefore upstream relative velocity will the difference between two velocities.

$(V_{wb})_{up}=\frac{distance}{upstream\_time} \\\\V_b-V_w=\frac{2000m}{20*60 sec} \\\\V_b-V_w= 1.67 \frac{m}{sec} \\ \\ V_b=1.67+V_w ----- > (1)$

2) Downstream relative velocity: Here the velocity of water helps the boat to speed up. so, downstream relative velocity will be addition of both the velocities.

$(V_{wb})_{down}=\frac{distance}{downstream\_time} \\\\V_b+V_w=\frac{2000m}{10*60 sec} \\\\V_b+V_w= 3.33 \frac{m}{sec} ----- > (2)$

By substituting $(1)$ in $(2)$ we get

$(1.67+V_w)+V_w=3.33\\ \\2V_w=3.33-1.67\\ \\2V_w=1.663\\\\V_w = 0.831\frac{m}{sec} \\ \\ V_w = 3 \frac{Km}{hr}$

∴Velocity of river water $V_w = 3 \frac{Km}{hr}$

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