Question

Elena has a boat that would go 9 miles per hour in still water. She travels downstream for a certain distance and then
back upstream to where she started. Elena notices that it takes her 4 hours to travel upstream and 2 hours to travel
downstream. The river's speed is r miles per hour. Write an expression that will help her solve for r.
Show Work

Answer 1

The expression $r = \frac{t_{u}-t_{d}}{t_{d}+t_{u}} \cdot u$ will help Elena to solve for the speed of the river.

In this case we know the absolute speeds of Elena for travelling upstream and downstream, which is a combination of the boat speed in still water ($u$), in miles per hour, and the speed of the river ($r$), in miles per hour, as well as travelling times for each case. Let suppose that boat travels at constant speed in both cases:

Upstream (against the river)

$u-r = \frac{s}{t_{u}}$ (1)

Downstream (with the river)

$u+r = \frac{s}{t_{d}}$ (2)

Where:

• $s$ - Distance, in miles.
• $t_{u}$ - Upstream time, in hours.
• $t_{d}$ - Downstream time, in hors.

We derive a new expression by eliminating $s$:

$(u+r)\cdot t_{d} = (u-r)\cdot t_{u}$

$(t_{u}-t_{d})\cdot u = (t_{d}+t_{u})\cdot r$

$r = \frac{t_{u}-t_{d}}{t_{d}+t_{u}} \cdot u$

The expression $r = \frac{t_{u}-t_{d}}{t_{d}+t_{u}} \cdot u$ will help Elena to solve for the speed of the river.

We kindly invite to see this question on uniform speed: https://brainly.com/question/17194484