Question 9 of 10, Step 1 of 16/10Correct0A boat can travel 44 mph in still water. If it travels 276 miles with the current in the same length of time it travels 252 miles against the current, what is the speed of thecurrent?

Question 9 of 10 Step 1 of 1610Correct0A boat can travel 44 mph in still water If it travels 276 miles with the current in the same length of time it travels 25 class=

Respuesta :

Let's use the variable v to represent the current speed and t to represent the length of time.

If the distance traveled when the boat is with the current is 276 miles, we have:

[tex]\begin{gathered} distance=speed\cdot time\\ \\ 276=(44+v)\operatorname{\cdot}t\\ \\ t=\frac{276}{44+v} \end{gathered}[/tex]

Then, when the boat is against the current, the distance is 252 miles, so:

[tex]\begin{gathered} 252=(44-v)\operatorname{\cdot}t\\ \\ t=\frac{252}{44-v} \end{gathered}[/tex]

Equating both values of t, we have:

[tex]\begin{gathered} \frac{276}{44+v}=\frac{252}{44-v}\\ \\ 252\operatorname{\cdot}(44+v)=276\operatorname{\cdot}(44-v)\\ \\ 11088+252v=12144-276v\\ \\ 252v+276v=12144-11088\\ \\ 528=1056\\ \\ v=\frac{1056}{528}=2 \end{gathered}[/tex]

Therefore the current speed is 2 mph.

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