a motor boat covers a certain distance downstream in a river is 5 hours it covers the same distance upstream in 6 hours the speed of water is 2 km per hour find the speed of the boat in still water
Answers
LET THE SPEED OF THE MOTORBOAT IN STILL WATER BE X km/hr
SPEED OF THE BOAT IN DOWNSTREAM IS (X +2) km/hr
TIME TAKEN TO COVER THE DISTANCE IN DOWNSTREAM IS 5 Hours
DISTANCE COVERED IN THE DOWNSTREAM = 5 *(X+2)
TIME TAKEN TO COVER THE DISTANCE IN UPSTREAM IS 6 HOURS
SPEED OF THE MOTORBOAT IN UPSTREAM IS (X-2)km/hr
DISTANCE COVERED IN THE UPSTREAM = 6*(X-2)
IN THE QUESTION DISTANCE IS FIXED, THEREFORE
5*(X+2)=6*(X-2)
5X + 10 = 6X - 12
6X - 5X = 10 + 12
X=22 km/hr
HENCE THE SPEED OF THE STREAM IS 22 KM/HR
I HOPE IT HELPS YOU!
Given :
Distance covered by motorboat downstream in 5 hours.
And it covers same distance upstream in 6 hours.
The speed of water is 2km/hr.
To find :
The speed of the boat in still water.
Solution :
Let's assume the speed of the boat in still water as x km/h.
Speed of water(given) = 2km/h
Speed of boat in downstream = (x+2) km/h
So, Distance covered in 5 hrs :
D= Speed x Time
=5 x (x + 2) km
= 5x + 10 km
•Speed of boat in upstream = (x - 2) km/h
So, Distance covered in 6 hrs : Speed x Time
= 6 x (x - 2) km
= 6x 12 km
Now, As is given that the boot covers the same distance upstream and downstream also.
Thus,
6x - 12 = 5x + 10
6x - 5x = 10 + 12
x = 22
Therefore x = 22 km/h that is the speed of water in still water.
Checking the answer :
•Distance covered in 5 hours in downstream = Speed x Time
D = 5(x + 2)
= 5(22 + 2)
= 110 + 10
= 120 km
•Distance covered in 6 hours in upstream = D=Speed x Time
= 6(x - 2)
= 6(22 - 2)
= 132 - 12
= 120 km.
Thus, in both the cases ,the distance is equal .Hence the Solution is correct.