Question

a motorboat whose speed is 18 kilometre per hour in still water takes 1 hour more to go 24 kilometre upstream then to return downstream to the same spot the speed of stream is​

Answer 1

Solution:

Speed of boat in still water = 18 km/h

Let speed of the stream = s

Speed of boat upstream = speed of boat in still water - speed of stream = 18 - s

Speed of boat downstream = speed of boat in still water + speed of stream = 18 + s

Time taken for upstream = Time taken to cover downstream + 1

Distance (upstream) / Speed (upstream) = Distance (downstream) / Speed (downstream) + 1

( 24 / 18 - s ) = ( 24 / 18 + s ) + 1

=> 24( 18 + s ) = 24( 18 - s ) + ( 18 + s )( 18 - s )

=> s^2 + 48s - 324 = 0

=> s^2 + 54s - 6s - 324 = 0

=> ( s + 54 )( s - 6 ) = 0

Therefore, s = 6, -54

Negative value cannot be taken.

Thus, s = 6 km/h

Thus, the speed of stream is 6 km/h.

Answer 2

Answer:

Let the speed of stream be x km / hr

For upstream = ( 18 - x ) km / hr

For downstream = ( 18 + x ) km / hr

A.T.Q.

24 / 18 - x - 24 / 18 + x = 1

48 x = 324 - x²

x² + 48 x - 324 = 0

( x + 54 ) ( x - 6 ) = 0

x = - 54 or x = 6

Since speed can't be negative .

Therefore , speed of the stream is 6 km / hr .