Finding the speed of the boat assuming speed of river is constant speed to water.

Question

A motorboat heads upstream a distance of 24 miles on a river whose current is running at 3 miles per hour (mi/hr). The trip up and back takes 6 hours. Assuming that the motorboat maintained a constant speed relative to the water, what was its speed?

Answer 1

d = rt, so t = d/r

 

6 = 24/(r-3) + 24/(r+3)

 

6r² - 54 = 24r + 72 + 24r - 72

6r² - 48r - 54 = 0

6(x + 1)(x - 9) = 0

 

x + 1 = 0

x = -1

 

We can't have a negative speed.

 

x - 9 = 0

x = 9

 

Let's check...

 

6 = 24/(9-3) + 24/(9+3)

6 = 24/6 + 24/12

6 = 4 +:2

6 = 6

 

Check! The boat moves at 9 mph.