Calculate speed

Question

Boat travels 50 mi with current in 2hrs then travels 26 mi against current in 2hrs find speed of boat in still water and speed of the current

Answer 1

D = Distance = rate x time

 

Let  B = boat's speed in still water (mph)

      C = current speed (mph)

 

1) D = (B + C)*t 

    B + C = D/t = 50/2 = 25

    B  = 25 - C

 

2) D = (B - C)*t   or (B - C)*t  = D

    B - C = D/t                        substitute for B = 25 - C and solve for C

   (25 - C) - C = D/t

    25 - 2*C = D/t

   2*C = 25 - D/t = 25 - 26/2 = 25 - 13 = 12

 

C = 12/2 = 6 mph    speed of the current

 

B = 25 - C = 25 - 6 = 19 mph speed of the boat in still water