Respuesta :
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]
[tex]\begin{gathered} 30\text{ = }\frac{5y}{2}+\text{ }\frac{5y-10}{3} \\ 30\text{ = }\frac{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}[/tex]Substitute the value of y into equation (1)
[tex]\begin{gathered} 15\text{ + k = }\frac{5y}{2} \\ 15\text{ + k = }\frac{5(8)}{2} \\ 15\text{ + k = }\frac{40}{2} \\ 15\text{ + k = 20} \\ k\text{ = 20 - 15} \\ k\text{ = 5} \end{gathered}[/tex]The rate of the current = 5 mph
