Question

Aro diagrams his river rafting trip, estimating the time it will take him to paddle upstream against the current, and then back downstream with the current. His campsite destination is 5.2 miles upstream. Determine how fast Aro can paddle and how fast the river water is moving.

Upstream:

Downstream:

Use the fact that d = rt to write the system of equations that represents the scenario. Let x be the speed of Aro’s paddling and let y be the speed of the river.



Upstream:

5.2 = (
)



Downstream:

5.2 = (
)

Answer 1

The system of equations are:

Upstream: 5.2 = (x - y)t

Downstream: 5.2 = (x + y)t

To solve for x using elimination, we can add the upstream and downstream equations together:

10.4 = 2x

Solving for x, we get:

x = 5.2

5.2 = (5.2 - y)t

5.2 = 5.2t - yt

Solving for y, we get:

y = 0

Therefore, Aro's paddling speed is 5.2 miles per hour, and the speed of the river water is 0 miles per hour.