A boat goes 2, km upstream and 3, km downstre | vedclass

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

Question

(C) Let the speed of the boat in still water be $x\, km/hr$ and the speed of the stream be $y\, km/hr$.Upstream speed = $(x - y)\, km/hr$ and downstre

Vedclass · Accepted Answer

$\frac{135}{7}$

Vedclass · Answer

(C) Let the speed of the boat in still water be $x\, km/hr$ and the speed of the stream be $y\, km/hr$.Upstream speed = $(x - y)\, km/hr$ and downstream speed = $(x + y)\, km/hr$.Given,time = $	ext{distance} / 	ext{speed}$.For the first case: $\frac{2}{x-y} + \frac{3}{x+y} = \frac{20}{60} = \frac{1}{3} \implies \frac{6}{x-y} + \frac{9}{x+y} = 1$  ---$(1)$For the second case: $\frac{7}{x-y} + \frac{2}{x+y} = \frac{53}{60}$ ---$(2)$Let $u = \frac{1}{x-y}$ and $v = \frac{1}{x+y}$.$6u + 9v = 1$ ---$(3)$$7u + 2v = \frac{53}{60}$ ---$(4)$Multiplying $(3)$ by $2$ and $(4)$ by $9$:$12u + 18v = 2$$63u + 18v = \frac{477}{60} = 7.95$Subtracting the equations: $51u = 5.95 \implies u = \frac{5.95}{51} = \frac{595}{5100} = \frac{7}{60}$.So,$x - y = \frac{60}{7}$.Substituting $u$ in $(3)$: $6(\frac{7}{60}) + 9v = 1 \implies \frac{7}{10} + 9v = 1 \implies 9v = \frac{3}{10} \implies v = \frac{3}{90} = \frac{1}{30}$.So,$x + y = 30$.Adding $x - y = \frac{60}{7}$ and $x + y = 30$:$2x = \frac{60}{7} + 30 = \frac{60 + 210}{7} = \frac{270}{7}$.$x = \frac{135}{7}\, km/hr$.

$A$ boat goes $2\, km$ upstream and $3\, km$ downstream in $20$ minutes. It goes $7\, km$ upstream and $2\, km$ downstream in $53$ minutes. What is the speed (in $km/hr$) of the boat in still water?

Similar Questions

$A$ man can row at a speed of $4.5 \text{ km/hr}$ in still water to a certain upstream point and back to the starting point in a river which flows at $1.5 \text{ km/hr}$. Find his average speed for the total journey in $\text{km/hr}$.

$A$ boat travels upstream from $B$ to $A$ and downstream from $A$ to $B$ in $3$ $hrs$. If the speed of the boat in still water is $9$ $km/h$ and the speed of the current is $3$ $km/h$,the distance between $A$ and $B$ is......$km$.

$A$ boat covers $24 \text{ km}$ upstream and $36 \text{ km}$ downstream in $6 \text{ hours}$,while it covers $36 \text{ km}$ upstream and $24 \text{ km}$ downstream in $6 \frac{1}{2} \text{ hours}$. The velocity of the current is .... $\text{km/h}$.

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 $km/h$).

$A$ boat running downstream covers a distance of $20\, km$ in $2\, h$ while it covers the same distance upstream in $5\, h$. Then,the speed of the boat in still water is ....... $km/h$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module