Amotorboat 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:

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              

----> equation A            

going downstream                                  

----> equation B                            

Solve the system of equations by elimination                            

Adds equation A and equation B                                      

Find the value of x                                

therefore          

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

The rate of the current is 10 miles per hour