Question

2) A seat has a speed of 15 mph in seicher travels downstream from Greentown to Glenevon in 2/5 of an hour. It then goes back upstream from Glenevon to Colombia, which is 2 miles downstream, in 3/5 of an hour. Find the rate of the current.

Answer 1

Answer:

Rate of the current = 5 mph

Explanations:

The time taken to travel downstream from Greentown to Glenevon = 2/5 hours

The time taken to travel upstream from Glenevon to Columbia = 3/5 hours

Rate = Distance /time

Let the distance traveled = y miles

Rate of the downstream travel:

Rate = y ÷ 2/5

Rate = y x 5/2

Rate = 5y / 2

Rate of the upstream travel

Since the travel upstream from Glenevon to Columbia is 2 meters downstream:

Distance = y - 2

Rate = (y-2) ÷ 3/5

Rate = (y-2) x 5/3

Rate = 5(y-2)/3

Let the current rate be represented by k

The rate of the downstream travel will be:

15 + k = 5y/2...........(1)

The rate of the upstream movement will be:

15 - k = 5(y-2)/3............(2)

Add equations (1) and (2)

(15 + k) + (15 - k) = [5y/3] + [5(y-2)/3]

`\begin{gathered} 30\text{ = }(5y)/(2)+\text{ }(5y-10)/(3) \\ 30\text{ = }(15y+10y-20)/(6) \\ 30(6)\text{ = 15y + 10y - 20} \\ 180\text{ = 25y - 20} \\ 180\text{ + 20 = 25y} \\ 25y\text{ = 200} \\ y\text{ = 200/25} \\ y\text{ = 8} \end{gathered}`

Substitute the value of y into equation (1)

`\begin{gathered} 15\text{ + k = }(5y)/(2) \\ 15\text{ + k = }(5(8))/(2) \\ 15\text{ + k = }(40)/(2) \\ 15\text{ + k = 20} \\ k\text{ = 20 - 15} \\ k\text{ = 5} \end{gathered}`

The rate of the current = 5 mph