Question

A boat running upstream takes $7\text{hr}$ to cover a certain distance, while it takes $4\text{hr}$ to cover the same distance running downstream. What is ratio of the speed of boat in still water to the speed of water current?

• A. $11:3$
• B. $3:2$
• C. $7:3$
• D. Can't be determined

Answer 1

The correct option is A $11:3$

Let velocity of water current be $-v_w\hat{i}$
Let speed of boat be $v_b$
Velocity of boat w.r.t ground is given as
For upstream:
${\overrightarrow{v}}_{bg}=v_b\hat{i}+(-v_w\hat{i})=(v_b-v_w)\hat{i}$
Speed of boat upstream $=v_b-v_w$
For downstream:
${\overrightarrow{v}}_{bg}=-v_b\hat{i}+(-v_w\hat{i})=-(v_b+v_w)\hat{i}$
$\therefore$Speed of boat downstream$=(v_b+v_w)$

$\because \text{distance covered upstream}$
$=\text{distance covered downstream}$
$\Rightarrow (v_b-v_w)\times 7=(v_b+v_w)\times 4$
$\Rightarrow 7v_b-7v_w=4v_b+4v_w$
$\therefore \frac{v_b}{v_w}=\frac{11}{3}$