SOLUTION: The Smith family took a canoe 10 miles down the Allegheny River in 1 hour and 15 minutes. After lunch it took them 4 hours to return. Find the rate of the current. I have set

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: The Smith family took a canoe 10 miles down the Allegheny River in 1 hour and 15 minutes. After lunch it took them 4 hours to return. Find the rate of the current. I have set       Log On


   

Question 11412: The Smith family took a canoe 10 miles down the Allegheny River in 1 hour and 15 minutes. After lunch it took them 4 hours to return. Find the rate of the current.
I have set up a table with:
Distance = 10 both upstream and downstream
Canoe speed downstream = x + y
Canoe speed upstream = x - y
Time going downstream = 1 1/4 hour
Time going upstream = 4 hours
I just keep getting bogged down with the fractions when trying to solve by addition method or substitution method.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Using the distance formuls:
d+=+rt where: d = distance (10 miles), r = speed (rate) and t = time.
Downstream trip:
10+=+r1%281.25%29
r1+=+8mph
Upstream trip:
10+=+r2%284%29
r2+=+2.5mph
Let x = speed of canoe and y = rate of the current.
Downstream:
x%2By+=+8
Upstream:
x-y+=+2.5 Rewrite as: x+=+y+%2B+2.5 and substitute into the above.
%28y%2B2.5%29+%2B+y+=+8 Simplify and solve for y.
2y+%2B+2.5+=+8 Subtract 2.5 from both sides.
2y+=+5.5 Divide both sides by 2.
y+=+2.75 mph is the rate of the current.