Question

A boat takes 60 minutes less to travel 40 km downstream than to travel the same distance upstream. if the speed of the boat in still water is 15 kmph. what is the speed of the stream

Answer 1

Let the speed of Stream be y km/h then
Let the time taken to go 40 km downstream be t hours        
then the time taken to go 40 km upstream is (t+1) hours  .........since 60 min=1 hr

Also,
time = distance/ speed

so,
     t=40/(15+y)
     t+1=40/(15-y)

Now,

=>40/(15-y) - 40/(15+y) = 1
=> y²+80y - 225 =0;

we get,

      y= 2.72 km/h

so the speed of the stream is 2.72 km/h

Answer 2

Given :

Let the speed of the stream be X km/h thenSpeed downstream =(15+x) km/hSpped upsstream =(15-x )km/h

40/(15-x) - 40/(15+x)=60/60

40(15+x)-40(15-x)=(15-x)²

600 +40x -600+40x= 225-x²

x² +80x -225=0

Solving the above quadratic equations we get :
X=( - b± √b²-4ac)/2a

here a=1
b= -80
c=225

b²-4ac= 6400-900 =5500

x=80± √5500/2

on solving for X we get, 

X=2.919 

Therefore speed of stream =2.919 km/hr