A boat covers a certain distance between two | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Let $d$ be the distance between the two spots,$v$ be the speed of the boat in still water,and $u$ be the speed of the river current.For downstream

Vedclass · Accepted Answer

$\frac{2 t_1 t_2}{t_1+t_2}$

Vedclass · Answer

(C) Let $d$ be the distance between the two spots,$v$ be the speed of the boat in still water,and $u$ be the speed of the river current.For downstream motion,the effective speed is $(v+u)$. Thus,$t_1 = \frac{d}{v+u} \Rightarrow d = (v+u)t_1 \dots (i)$For upstream motion,the effective speed is $(v-u)$. Thus,$t_2 = \frac{d}{v-u} \Rightarrow d = (v-u)t_2 \dots (ii)$Equating $(i)$ and $(ii)$,we get $(v+u)t_1 = (v-u)t_2$.$vt_1 + ut_1 = vt_2 - ut_2 \Rightarrow u(t_1+t_2) = v(t_2-t_1) \Rightarrow u = v\frac{t_2-t_1}{t_1+t_2}$.Substituting $u$ into equation $(i)$,$d = (v + v\frac{t_2-t_1}{t_1+t_2})t_1 = v(\frac{t_1+t_2+t_2-t_1}{t_1+t_2})t_1 = v(\frac{2t_2}{t_1+t_2})t_1$.The time taken in still water is $t = \frac{d}{v}$.Therefore,$t = \frac{v(\frac{2t_1t_2}{t_1+t_2})}{v} = \frac{2t_1t_2}{t_1+t_2}$.

$A$ boat covers a certain distance between two spots in a river taking $t_1$ hours going downstream and $t_2$ hours going upstream. What time will be taken by the boat to cover the same distance in still water?

Similar Questions

$A$ flag is mounted on a car moving due North with a velocity of $20 \, km/hr$. Strong winds are blowing due East with a velocity of $20 \, km/hr$. The flag will point in which direction?

Rain is falling vertically with a speed of $30 \,m/s$. A man rides a bicycle with a speed of $10 \,m/s$ from East to West direction. At what angle with the vertical does he see the rain falling?

An observer moves with a constant speed along the line joining two stationary objects. He will observe that the two objects

An aeroplane is to go along a straight line from $A$ to $B$,and back again. The relative speed with respect to wind is $V$. The wind blows perpendicular to the line $AB$ with speed $v$. The distance between $A$ and $B$ is $\ell$. The total time for the round trip is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module