Question

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.

Answer 1

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!