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ira [324]
3 years ago
6

A motor travels 10 mph in still water. The boat takes 4 hours longer to travel 48 miles going upstream than it does to travel 24

miles going downstream. Find the rate of the current.
Mathematics
1 answer:
Tanzania [10]3 years ago
6 0

Answer:

The rate of the current is 2 mph.

Step-by-step explanation:

When the boat travels upstream we have:

v_{T_{1}} = v_{b} - v_{c}                      

\frac{x_{1}}{t_{1}} = v_{b} - v_{c}    

Where:

v_{T}: is the total speed

v_{b}: is the speed of the boat = 10 mph

v_{c}: is the speed of the current

x: is the distance

t: is the time

And when the boat travel downstream we have:

v_{T_{2}} = v_{b} + v_{c}        

\frac{x_{2}}{t_{2}} = v_{b} + v_{c}                              

Since the boat takes 4 hours longer to travel 48 miles going upstream than it does to travel 24 miles going downstream we have:

\frac{x_{1}}{t + 4} = v_{b} - v_{c}   (1)

\frac{x_{2}}{t} = v_{b} + v_{c}   (2)

By adding equation (1) with (2):

\frac{x_{1}}{t + 4} + \frac{x_{2}}{t} = 2v_{b}

tx_{1} + (t+4)x_{2} - 2v_{b}t(t+4) = 0

48t + 24(t+4) - 2*10t(t+4) = 0

By solving the above equation for t we have:

t = 2 h      

Now, by entering "t" into equation (2) we have:

\frac{24 miles}{2 h} = 10 mph + v_{c}  

v_{c} = 2 mph

               

Therefore, the rate of the current is 2 mph.

I hope it helps you!  

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