A motorboat takes 5 hours to travel 450km going upstream. The return trip takes 3 hours going downstream. What is the rate of the boat in still water and what is the rate of the current?

Question

anonymous · Answer

The rate of the boat will be 120km/hr and the stream will b3 30km/hr. Try it.

callisto · Answer

Let rate of boat in still water be x and rate of current be y.
Using the formula $\large speed = \frac{distance}{time}$
For upstream: 
$$\frac{450}{x-y} = 5 $$$$450 = 5(x-y) $$$$450 = 5x-5y \ \ -(1)$$

For downstream:
$$\frac{450}{x+y} = 3 $$$$450 = 3(x+y)$$$$450 = 3x+3y  \ \ -(2)$$

(1)x3 + (2)x5
     450x3 = 3(5x-5y)
+  450x5 = 5(3x+3y)
------------------
    3600 = 30x

 Divide both sides by coefficient of x, that is 30
   3600 / 30 = 30x / 30 
              x    = 120 km/h

Put x =120 into (1)
450 = 5(120) - 5y
450 = 600 - 5y
-150 = -5y
y = 30 km/h

So, rate of boat in still water is  120km/h and rate of current is 30km/h.