This is the basic and exam oriented question from linear equations in two variables we have to find the speed of current and the speed of the sailor if the sailor goes 8 km downstream in 40 minutes and returns in 1.
Kindly give me a detailed solution of this question
RS Aggarwal, Class 10, chapter 3E, question no 35
Let the speed of the sailor in still water be x km/hr and speed of the current be y km/hr.
Then, speed of sailor downstream =x+y km/hr and speed of sailor upstream =x−y km/hr.
Distance covered =8 km.
Also, Time=Distance/speed
From the given information, we have,
8/(x+y)=40/60 and 8/(x−y)=1
or,8/(x+y)=40/60
=>8/(x+y)=2/3
=>24=2(x+y)
=>x+y=12....(i)
Also,8/(x−y)=1
=>x=8+y....(ii)
Substituting (ii) in (i), we get,
x+y=12
=>8+y+y=12
=>2y=4
=>y=2
Substituting y=2 in equation (ii), we get,
x=8+y
=>x=8+2
=>x=10
Therefore, speed of sailor in still water =x=10 km/hr
and speed of the current =y=2 km/hr.