A sailor goes 8 km downstream in 40 minutes and returns in 1 hours. Determine the speed of the sailor in still water and the speed of the current.
Answers
SOLUTION :
Given :
Distance cover by a sailor upstream= 8 km
Distance cover by a sailor downstream = 8 km
Let the speed of the sailor in still water be x km/hr and the speed of the current be y km/hr
Speed upstream = (x- y) km/hr
Speed downstream = (x + y)km/hr
Time taken to cover 8 km downstream = 8/( x+ y) hrs
[ Time = distance/speed]
Time taken to cover 8 km upstream = 8/(x−y) hrs
Time taken to cover 8 km downstream in 40 minutes = 40/60 hours = 2/3hrs
8/(x+y)= 2/3
8×3 = 2(x+y)
24 = 2x + 2y
24 = 2(x +y)
24/2 = x + y
12 = x+y …………..…(1)
Time taken to cover 8 km upstream in 1 hour
8/(x−y) = 1
8 = (x - y) ……..…..(2)
On adding eq 1 & 2,
12 = x+y
8 = x - y
-------------
20 = 2x
x = 20/2
x= 10
On substituting x = 10 in equation (1) we get,
x + y = 12
10 + y = 12
y = 12 - 10
y = 2
Hence, the speed of sailor is 10 km/hr & Speed of Current is 2 km/hr.
HOPE THIS ANSWER WILL HELP YOU...
Given :
Distance cover by a sailor upstream= 8 km
Distance cover by a sailor downstream = 8 km
Let the speed of the sailor in still water be x
km/hr
Let the speed of the current be y km/hr
Speed upstream = (x- y) km/hr
Speed downstream = (x + y)km/hr
Time taken to cover 8 km downstream = 8/( x+ y) hrs
We already know that:
Time = distance/speed
ACCORDING TO THE QUESTION;
Time taken to cover 8 km upstream = 8/(x−y) hrs
Time taken to cover 8 km downstream in 40 minutes
= 40/60 hrs= 2/3hrs
=======================
8/(x+y)= 2/3
8×3 = 2(x+y)
24 = 2x + 2y
24 = 2(x +y)
24/2 = x + y
12 = x+y >>>>>>(1)
Time taken to cover 8 km upstream in 1 hour :-
8/(x−y) = 1
8 = (x - y) >>>>>(2)
On adding Equation
x+y=12
x-y=8
_________
20 = 2x
_________
x = 20/2
x= 10
Now...
On substituting x = 10 in equation (1)
x + y = 12
10 + y = 12
y = 12 - 10
y = 2
Conclusion:-
the speed of sailor is 10 km/hr .
Speed of Current is 2 km/hr.