Question

A motorboat covers a distance downstream in a river 5 hours, it covers the same distance upstream in 5 and half hours, find the speed of the boat in still water, if the speed of the stream is 1.5 km/h?

Answer 1

Question :-

A motorboat covers a distance downstream in a river 5 hours, it covers the same distance upstream in 5 and half hours, find the speed of the boat in still water, if the speed of thestream is 1.5 km/h?

Answer :-

• Speed of boat in still water is 31.5 km/hr

Solution :-

Let the speed of boat in still water = xkm/hr

and the distance be y km/hr

we know that distance = speed x time

Therefore,

Speed in downstream = ( x + 1.5 ) km/hr

Speed in upstream = ( x - 1.5 ) km/hr

According to the question ,

s = ( x +1.5 ) × 5....................(i)

s = ( x − 1.5 ) × 5.5...............(ii)

Solving equations (i) and (ii)

$\large \tt s=(5x+7.5)=(5.5x−8.25)$

$\\ \large \tt⇒5x+7.5=5.5x−8.25$

$\\ \large \tt⇒5.5x−5x=7.5+8.25$

$\\ \large \tt⇒0.5x=15.75$

$\\ \therefore \tt x=\frac{ \cancel{15.75}}{ \cancel{0.5}} = 31.5$

∴ Speed of boat in still water is 31.5 km/hr