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

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) (Show Source): You can put this solution on YOUR website!
Using the distance formuls:
where: d = distance (10 miles), r = speed (rate) and t = time.
Downstream trip:

mph
Upstream trip:

mph
Let x = speed of canoe and y = rate of the current.
Downstream:

Upstream:
Rewrite as: and substitute into the above.
Simplify and solve for y.
Subtract 2.5 from both sides.
Divide both sides by 2.
mph is the rate of the current.
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