In a stream running at 2 km/h,a motorboat go | vedclass

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

Question

(A) Let the speed of the motorboat in still water be $x \ km/h$.Given the speed of the stream $y = 2 \ km/h$.The speed upstream is $(x - 2) \ km/h$ an

Vedclass · Accepted Answer

$22$

Vedclass · Answer

(A) Let the speed of the motorboat in still water be $x \ km/h$.Given the speed of the stream $y = 2 \ km/h$.The speed upstream is $(x - 2) \ km/h$ and the speed downstream is $(x + 2) \ km/h$.The total time taken is $33 \ minutes = \frac{33}{60} \ hours = \frac{11}{20} \ hours$.According to the problem: $\frac{6}{x-2} + \frac{6}{x+2} = \frac{11}{20}$.$6 \left( \frac{x+2+x-2}{x^2-4} ight) = \frac{11}{20} \Rightarrow 6 \left( \frac{2x}{x^2-4} ight) = \frac{11}{20}$.$12x 	imes 20 = 11(x^2 - 4) \Rightarrow 240x = 11x^2 - 44$.$11x^2 - 240x - 44 = 0$.$11x^2 - 242x + 2x - 44 = 0 \Rightarrow 11x(x - 22) + 2(x - 22) = 0$.$(x - 22)(11x + 2) = 0$.Since speed cannot be negative,$x = 22 \ km/h$.

In a stream running at $2 \ km/h$,a motorboat goes $6 \ km$ upstream and back again to the starting point in $33 \ minutes$. Find the speed of the motorboat in still water. (in $km/h$)

Similar Questions

$A$ man can row $30 \text{ km}$ downstream and return in a total of $8 \text{ h}$. If the speed of the boat in still water is $4$ times the speed of the current,then the speed of the current is ....... $\text{km/h}$.

Rohit can row a certain distance downstream in $8$ $hours$ and return the same distance in $12$ $hours$. If the stream flows at the rate of $5$ $km/hr$,find the speed of Rohit in still water (in $km/hr$).

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:

$A$ man swimming in a stream which flows at $1 \frac{1}{2} \text{ km/h}$ finds that in a given time he can swim twice as far with the stream as he can against it. At what rate does he swim? (in $\text{km/h}$)

$A$ 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:

Vedclass Test Series

Exam Paper Generator

Online Exam Module