Word problem

Question

Bill rowed 30 km upstream against a 2km/h current and back again in a total of 8 hours. What is the rate in still water?

Answer 1

Let x = speed of boat in still water

 

x + 2 = speed with the current

x - 2 = speed against the current

 

Distance = (Rate)(Time)

 

So, Time = Distance/Rate

 

Time upstream + Time downstream = Total time

 

30/(x+2) + 30/(x-2) = 8

 

Multiply both sides by the LCD, (x+2)(x-2) 

 

30(x-2) + 30(x+2) = 8(x+2)(x-2)

 

60x = 8(x²-4)

 

8x² - 60x - 32 = 0

 

Divide by 4:  2x² - 15x - 8 = 0

 

                      (2x + 1)(x - 8) = 0

 

                      x = -1/2 or 8

 

Since x can't be negative, x = 8 km/hr