Question

1. Two boats leave a dock at the same time, but they are traveling in opposite
directions. The longest time either boat is capable of traveling without stopping is 6
hours. Boat F travels 200 miles north in x-1 hours, and boat G travels 160 miles south in
x hours.

Answer 1

The boat F spends a time of 3 hours to travel 200 miles north and the boat G spends a time of 4 hours to travel 160 miles south.

How to apply uniform motion to determine the travel time of two boats

In this question we suppose that each boat travels at constant velocity. In this case and dimensionally speaking, the speed ($v$), in miles per hour, is equal to the traveled distance ($s$), in miles, divided by time ($t$), in hours. Then, this problem can be represented by the following expression:

$\frac{200}{x-1} = \frac{160}{x}$   (1)

Now we clear $x$ within (1):

$200\cdot x = 160\cdot (x-1)$

$x = 4$

The boat F spends a time of 3 hours to travel 200 miles north and the boat G spends a time of 4 hours to travel 160 miles south. $\blacksquare$

Remark

The statement is incomplete and poorly formatted. The complete statement is shown below:

Two boats leave a dock at the same time, but they are traveling in opposite directions at same speed. The longest time either boat is capable of traveling without stopping is 6 hours. Boat F travels 200 miles north in $x-1$ hours, and Boat G travels 160 miles south in $x$ hours. How much time does each boat travel?

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