While Brendan is vacationing with his family at the cabin, they take a motorboat on the river. The motorboat travels

18 miles per hour in still water.

1. Let w represent the speed of the river current in miles per hour. Write an expression for how fast the

motorboat is able to go downstream (with the current) Write another expression for how fast the motorboat is

able to go upstream (against the current).

2. The motorboat travels 49 miles upstream in the same time it takes to travel 77 miles downstream. What is the

speed of the current w? Use the Elimination Method to solve.

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vijayalalitha vijayalalitha · Answer 1 · 2020-02-25T13:23:51+01:00

Part 1: The speed of the boat traveling downstream is [tex](18+w)[/tex] miles per hr.

The speed of the boat traveling upstream is [tex](18-w)[/tex] miles per hr.

Part 2: The speed of the current is 4 miles per hour.

Explanation:

Part (1): The motorboat travels 18 miles per hour in still.

Let w represents the speed of the current.

When the boat travels downstream, the speed of the current will get added to the speed of the boat.

Thus, the expression can be written as [tex](18+w)[/tex] miles per hr

Hence, the speed of the boat traveling downstream is [tex](18+w)[/tex] miles per hr.

When the boat travels upstream, the speed of the current will get subtracted to the speed of the boat.

Thus, the expression can be written as [tex](18-w)[/tex] miles per hr.

Hence, the speed of the boat traveling upstream is [tex](18-w)[/tex] miles per hr.

Part (2): The boat travels 49 miles upstream in the same time it takes to travel 77 miles downstream.

The distance formula is given by [tex]distance $=$ speed $\times$ time[/tex]

Substituting, we have,

[tex]49=(18-w)t\\49=18t-wt[/tex] ---------------(1)

[tex]77=(18+w)t\\77=18t+wt[/tex] ---------------(2)

Solving using elimination method,

[tex]49=18 t-w t\\77=18 t+w t\\-------\\126=36t[/tex]

Dividing both sides by 36, we have,

[tex]t=3.5[/tex]

Substituting [tex]t=3.5[/tex] in [tex]$49=18 t-w t$[/tex], we get,

[tex]49=18(3.5)-w (3.5)\\[/tex]

[tex]49=63-3.5w\\[/tex]

[tex]-14=-3.5w\\[/tex]

[tex]4=w[/tex]

Thus, the speed of the current is [tex]w=4[/tex] miles per hour.