A boat travels 60 km downstream and 20 km ups | vedclass

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

Question

(B) Let the speed of the boat in still water be $x 	ext{ km/hr}$ and the speed of the stream be $y 	ext{ km/hr}$.Downstream speed $= (x+y) 	ext{ km

Vedclass · Accepted Answer

$16$

Vedclass · Answer

(B) Let the speed of the boat in still water be $x 	ext{ km/hr}$ and the speed of the stream be $y 	ext{ km/hr}$.Downstream speed $= (x+y) 	ext{ km/hr}$.Upstream speed $= (x-y) 	ext{ km/hr}$.According to the problem:$\frac{60}{x+y} + \frac{20}{x-y} = 4$  --- $(i)$$\frac{40}{x+y} + \frac{40}{x-y} = 6$  --- $(ii)$Let $u = \frac{1}{x+y}$ and $v = \frac{1}{x-y}$.$60u + 20v = 4 \Rightarrow 15u + 5v = 1$ --- $(iii)$$40u + 40v = 6 \Rightarrow 20u + 20v = 3$ --- $(iv)$Multiplying $(iii)$ by $4$: $60u + 20v = 4$.Subtracting $(iv)$ from this: $(60u + 20v) - (40u + 40v) = 4 - 6 \Rightarrow 20u - 20v = -2 \Rightarrow 10u - 10v = -1$.Solving the system,we get $u = \frac{1}{20}$ and $v = \frac{1}{10}$.$x+y = 20$ and $x-y = 10$.Adding the two equations: $2x = 30 \Rightarrow x = 15$.Subtracting: $2y = 10 \Rightarrow y = 5$.Wait,re-evaluating the system: $15u + 5v = 1$ and $20u + 20v = 3$. From $(iii)$,$5v = 1 - 15u \Rightarrow 20v = 4 - 60u$. Substitute into $(iv)$: $20u + 4 - 60u = 3 \Rightarrow -40u = -1 \Rightarrow u = \frac{1}{40}$.Then $5v = 1 - 15(\frac{1}{40}) = 1 - \frac{3}{8} = \frac{5}{8} \Rightarrow v = \frac{1}{8}$.$x+y = 40$ and $x-y = 8$.$2x = 48 \Rightarrow x = 24$.$2y = 32 \Rightarrow y = 16$.The speed of the stream is $16 	ext{ km/hr}$.

$A$ boat travels $60$ km downstream and $20$ km upstream in $4$ hours. The same boat travels $40$ km downstream and $40$ km upstream in $6$ hours. What is the speed (in $km/hr$) of the stream?

Similar Questions

The speed of a boat in still water is $10\, km/h$. It covers an upstream distance of $45\, km$ in $6\, h$. The speed (in $km/h$) of the stream is:

$A$ boat moves downstream at the rate of $1 \, km$ in $10 \, minutes$ and upstream at the rate of $4 \, km/h$. What is the velocity of the current (in $km/h$)?

$A$ motorboat travelling at some speed can cover $25\, km$ upstream and $39\, km$ downstream in $8\, h$. At the same speed,it can travel $35\, km$ upstream and $52\, km$ downstream in $11\, h$. The speed of the stream is........$km/h$.

The speed of a boat in still water is $6\, km/h$ and the speed of the stream is $1.5\, km/h$. $A$ man rows to a place at a distance of $22.5\, km$ and comes back to the starting point. Find the total time taken by him (in $hours$).

Speed of a man is $10 \text{ km/h}$ in still water. If the rate of current is $3 \text{ km/h}$,then the effective speed of the man upstream is ....... $\text{km/h}$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module