P,Q,and R are three towns on a river that flo | vedclass

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

Question

(A) Let the distance between $P$ and $Q$ be $d$. Since $Q$ is equidistant from $P$ and $R$,the distance between $Q$ and $R$ is also $d$. The total dis

Vedclass · Accepted Answer

$5:3$

Vedclass · Answer

(A) Let the distance between $P$ and $Q$ be $d$. Since $Q$ is equidistant from $P$ and $R$,the distance between $Q$ and $R$ is also $d$. The total distance from $P$ to $R$ is $2d$.Let $x$ be the speed of the boat in still water and $y$ be the speed of the river.Time taken to row from $P$ to $Q$ and back is $10$ $hours$:$\frac{d}{x+y} + \frac{d}{x-y} = 10 \quad \dots (1)$Time taken to row downstream from $P$ to $R$ is $4$ $hours$:$\frac{2d}{x+y} = 4 \Rightarrow d = 2(x+y) \quad \dots (2)$From equation $(1)$:$d \left( \frac{x-y+x+y}{(x+y)(x-y)} ight) = 10 \Rightarrow 2xd = 10(x^2 - y^2) \Rightarrow xd = 5(x^2 - y^2)$Substitute $d = 2(x+y)$ from equation $(2)$ into the expression:x($2$(x+y)) = $5$(x+y)(x-y)Since $x+y 
eq 0$,we can divide both sides by $(x+y)$:$2x = 5(x-y) \Rightarrow 2x = 5x - 5y \Rightarrow 3x = 5y$Therefore,$\frac{x}{y} = \frac{5}{3}$.

$P$,$Q$,and $R$ are three towns on a river that flows uniformly. $Q$ is equidistant from $P$ and $R$. $I$ row from $P$ to $Q$ and back in $10$ $hours$,and $I$ can row downstream from $P$ to $R$ in $4$ $hours$. Compare the speed of my boat in still water with that of the river.

Similar Questions

Speed of a boat is $5 \, km/h$ in still water and the speed of the stream is $3 \, km/h$. If the boat takes $3 \, h$ to go to a place and come back,the distance of the place is ....... $km$.

$A$ man swims downstream a distance of $15\, km$ in $1\, h$. If the speed of the current is $5\, km/h$,the time taken by the man to swim the same distance upstream is

Speed of a motorboat in still water is $45\, km/h$. If the motorboat travels $80\, km$ along the stream in $1\, h\, 20\, min$,then the time taken by it to cover the same distance against the stream will be:

$A$ motor boat,whose speed is $15 \text{ km/hr}$ in still water,goes $30 \text{ km}$ downstream and comes back in a total of $4 \text{ hours } 30 \text{ minutes}$. The speed of the stream (in $\text{km/hr}$) is:

When the speed of a boat in still water is $4\, km/h$ and the rate of stream is $2\, km/h$,find the upstream speed of the boat (in $km/h$).

Vedclass Test Series

Exam Paper Generator

Online Exam Module