If columbus rows 20 km upstream in 4 hours and 21 km downstream in 3 hours, then the speed of the stream is
Answers
Answer:
1 kmph
Explanation:
Speed of stream = 1/2 [ D - U ]
= 1/2 [ 21/3 - 20/4 ]
= 1/2 [ 7 - 5 ]
= 1/2 [ 2 ]
= 1 kmph
Given,
Time taken by Columbus to travel 20 km upstream is = 4 hours
Time taken by Columbus to travel 21 km downstream is = 3 hours
To find,
The speed of the stream.
Solution,
We can simply solve this mathematical problem using the following process:
Let us assume that the actual speed of the boat be x km/hr and the speed of the stream be y km/hr.
Now,
While traveling upstream;
Net speed of the boat
= actual speed of the boat - speed of the stream
= (x-y) km/hr (Equation 1)
Also, as per the question;
Net speed of the boat while traveling upstream
= Distance covered / time taken
= 20 km / 4 hours
= 5 km/hr (Equation 2)
On equating equations 1 and 2, we get;
Net speed of the boat while traveling upstream
= (x-y) km/hr = 5 km/hr (Equation 3)
Similarly,
While traveling downstream;
Net speed of the boat
= actual speed of the boat + speed of the stream
= (x+y) km/hr (Equation 4)
Also, as per the question;
Net speed of the boat while traveling upstream
= Distance covered / time taken
= 21 km / 3 hours
= 7 km/hr (Equation 5)
On equating equations 4 and 5, we get;
Net speed of the boat while traveling upstream
= (x+y) km/hr = 7 km/hr (Equation 6)
Now, adding equations 3 and 6, we get;
(x-y) + (x+y) = 5+7
=> 2x = 12
=> x = 6 km/hr
Substituting the value of x in equation 6, we get;
6 + y = 7
=> y = 1 km/hr
Hence, the speed of the stream is 1 km/hr.