Question

A motorboat takes 5 hours to travel 150 miles going upstream. The return trip takes 3 hours going downstream. What is the rate of the boat in still water and what is the rate of the current?
Rate of the boat in still water:

Rate of the current:

Answer 1

Answer:

The rate of the boat in still water is 40 miles per hour

The rate of the current is 10 miles per hour

Step-by-step explanation:

we know that        

The speed or rate is equal to divide the distance by the time

Let

x ----> the rate of the current (miles per hour)          

y ----> the rate of the boat in still water (miles per hour)        

we have that          

going upstream              

$y-x=\frac{150}{5}$        

$y-x=30$ ----> equation A            

going downstream                                  

$y+x=\frac{150}{3}$                            

$y+x=50$ ----> equation B                            

Solve the system of equations by elimination                            

Adds equation A and equation B                                      

$y-x=30\\y+x=50\\------\\y+y=30+50\\2y=80\\y=40$                    

Find the value of x                                

$y+x=50$                

$40+x=50$            

$x=10$          

therefore          

The rate of the boat in still water is 40 miles per hour      

The rate of the current is 10 miles per hour