Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • A motorboat whose speed is 18 km/hr in still water takes one hour more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream.     <div style=

A motorboat whose speed is 18 km/hr in still water takes one hour more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream.

 

 

 
 
 
 
 

Answers (1)

Given \rightarrow Speed of boat in still water (U) = 18 km/hr
One way distance (d) = 24 km
Time difference = 1 hour
Let velocity of river tream be \vartheta
\Rightarrow velocity of boat upstream = U-\vartheta
\Rightarrow velocity of boat downstream= U+\vartheta
We know \rightarrow time= \frac{distance}{velocity}
\Rightarrow According to question
     \frac{d}{U-\vartheta }-\frac{d}{U+\vartheta }= 1
\Rightarrow \frac{24}{18-\vartheta }-\frac{24}{18+\vartheta }= 1
\Rightarrow 24\left [ \frac{1}{\left ( 18-\vartheta \right )}-\frac{1}{\left ( 18+\vartheta \right )} \right ]= 1
\Rightarrow 24\left ( \frac{18+\vartheta -18+\vartheta }{\left ( 18-\vartheta \right )\left ( 18+\vartheta \right )} \right )= 1
\Rightarrow 24\times 2\vartheta = 18^{2}-\vartheta ^{2}
\Rightarrow \vartheta ^{2}+48\vartheta -324= 0
\Rightarrow \vartheta = \frac{-48\pm \sqrt{48^{2}-4\times 1\times \left ( -324 \right )}}{2\times 1}= \frac{-48\pm \sqrt{3600}}{2}
\Rightarrow \vartheta = \frac{-48\pm 60}{2}\Rightarrow \vartheta = -54,6
Since \vartheta can not be - ve
Hence velocity of stream = 6 km/hr

Posted by

Safeer PP

View full answer

Similar Questions

Trending Articles/News

anam-khan

CBSE Class 10 board exams twice a year ‘relief’ or ‘burden’? Parents, schools share mixed views
anam-khan

CBSE Class 10 exams twice a year from 2026; 64.4% students in favor, second attempt optional

Latest Question