Question

A boat traveled 240 miles downstream and back. The trip downstream took 12 hours. The trip back took 24 hours. What is the speed of the boat in still water? What is the speed of the current?

Answer 1

Answer:

rate boat = 15 mph

rate current = 5 mph

explanation:

d = r * t

t = d/r

240 / (r_boat + current) = 12       Multiply both sides by r_boat + r_current.

240 = 12(r_boat + current)

240/ (r_boat - current) = 24       Multiply both sides by r_boat - r_current

240 = 24*(r_boat - current)    

Since the distances are the same in both equations, you can equate the right side of each.

12 (r_boat + current) = 24(r_boat - current)     Divide by 12

r_boat + current  = 2 (r_boat - current)             Remove the brackets.

r_boat  + current = 2*r_boat - 2* current          add 2 currents to both sides

r_boat  + 3currents = 2*r_boat                          Subtract r_boat both sides

3 currents = r_boat.

240 = 12*(r_boat + current.                               Divide by 12

20 = r_boat + current                                        Put 3 currents in for r_boat

20 = 3currents + 1 current                                Combine

20 = 4 currents                                                  Divide by 4

5 = current

The rate of the current = 5 miles / hour

3 currents = r_boat

3*5 = rate_boat

15 = rate of the boat