Question

a boat goes downstream and covers distance between two ports in 4 hours , while it covers same distance upstream in 5 hours . what is speed of boat in still water . if speed of stream is 2km/hour

Answer 1

Let the speed of boat be x km/hr


Given, speed of stream = 2 km/hr





Given, time taken while going to downstream = 4 hours

Given, time taken while going to upstream = 5 hours




According to the quetion,


$\bold{ \large{While \: \: going \: \: downstream,} Speed \: \: of \: \: boat = ( x + 2 )} \\ \\ \\ \mathbf{we \: know \: \: speed \: = \frac{distance }{time} }$



Hence,



$\frac{distance }{4} = (x + 2) km \: \: \: \\ \\ => distance \: = 4(x + 2) \: \: km \: \\ \\ => distance \: = (4x + 8 )\: \: \: km \: \: \: \: \: \: \: \: --------: ( \: 1 \: ) equation$




$\bold{ \large{while \: going \: \: upstream} \: \: \: speed \: of \: \: boat \: = ( x - 2)km \: per \: hour} \\ \\ \\ => \frac{distance}{time} = x - 2 \\ \\ => distance \: =5 (x - 2) \\ \\ = > distance \: = (5x - 10)km \: \: \: \: \: \: \: \: - - --- - ( \: 2 \: ) \: equation$


Distance can't be change, it will remain same, so putting the value of distance from both equations

=> Distance = Distance

=> 4x + 8 = 5x - 10

=> 8 + 10 = 5x - 4x

=> 18 = x

$=> \frac{18}{1} = x$

Hence, Speed of boat is ( 18) km/hr

Answer 2

Let the speed of the boat in still water be x km/hr.

Given that speed of the stream is 2km/hr.

Downstream speed = (x + 2)km/hr.

Upstream speed = (x - 2)km/hr.

Given that boat goes downstream in 4 hours and upstream in 5 hours.

= > 4(x + 2) = 5(x - 2)

= > 4x + 8 = 5x - 10

= > 4x - 5x = -10 - 8

= > -x = -18

= > x = 18.

Therefore, the speed of the boat in still water is 18 km/hr.

Hope this helps!