Solve with simultaneous equations

Question

Solve with simultaneous equations

A boat travels 210 miles downstream and back. The trip down took 10 hours the trip back took 20 hours. What is the speed of the boat in still water. What is the speed of the current?

Answer 1

Downstream:   105 = (R+S)*10 = 10R +10S

Upstream        105 = (R-s)*20 = 20R - 20S

 

 

        Multiplies the top equation by 2:

                  210 = 20R + 20S

                  105 = 20R - 20S

 

adds them together:

               315 = 40R

 

              R = 315/40 = 63/8 = 7 and 7/8 = 7.875 mph

 

  Substitutes into the 2nd equation:

              105 = 20(63/8) - 20S

 

             105 = 5(63)/2 - 20 S

 

             105 = 315/2 - 20 S

 

             105 - 315/2 = -20 S

 

             (210 - 315)/2 = -20 S

 

               -105/2 = -20 S

 

              105/40 = S

 

              21/8 = S

 

             S = 2 and 5/8 mph = 2.625 mph

 

 

  The speed of the boat is 7 and 7/8 mph = 7.875 mph

 The speed of the current is 2 and 5/8 mph = 2.625 mph

 

 CHECK:

  downstream:

   10* (7 and 7/8 + 2 and 5/8)  = 10 * (9 and 12/8) = 10 * (9 and 3/2) = 10 * (10 and 1/2) = 10* (21/2) = 5*21 = 105

   

  upstream:

   20* (7 and 7/8 - 2 and 5/8)  = 20 * (6 and 15/8 - 2 and 5/8) = 20 * (4 and 10/8) = 20 * (4 and 5/4) = 20 * (5 and 1/4)

                                       = 20 * (21/4) = 5*21 = 105