A man can row down a 10 mile stream 2 hours and up in 5 hours. what is his average rate, in miles per hour,for the entire trip?
Answers
Answer:
3.5 miles/hour
Explanation:
Let the speed of the stream = y
And the speed of the man rowing = x
We need to find the speed of the man rowing, i.e., we need to find 'x'.
We know that: speed = distance/time
=> time = distance/speed
In the first case, the man is rowing downstream. So, the resultant speed will be speed of stream + speed of boat = (x + y)
In this case, time taken is 2 hours.
=> 2 = 10miles/(x+y)
=> 2 = 10/(x+y)
=> x + y = 10/2 = 5
x + y = 5 -------(i)
In the second case, the man is rowing upstream ( against the current). So, resultant speed = x - y
In this case, time taken is 5 hours
=> 5 = 10/(x - y)
=> x - y = 10/5 = 2
x - y = 2 ------(ii)
On adding (i) and (ii),
2x + y - y = 5 + 2 = 7
2x = 7
x = 7/2 = 3.5
Therefore, tje average speed of the man for the duration of the trip was 3.5miles/hour