Question

A motorboat takes 4 hours to travel 128mi going upstream. the return trip takes 2 hours going downstream. what is the rate of the boat in still water and what is the rate of the current?

Answer 1

Answer:

Rate of the boat in still water  =  48 mile/hr

Rate of the current = 16 mile/hr

Step-by-step explanation:

Let the rate of the boat in still water  be x and rate of the current be y.

Distance = 128 miles

Upstream rate = x - y

Downstream rate  = x + y

Time taken to travel upstream $=\frac{128}{x-y} = 4$

                           x - y = 32 ------------------eqn 1

Time taken to travel downstream $=\frac{128}{x+y} = 2$

                           x + y = 64 ------------------eqn 2

eqn 1 + eqn 2

               x - y + x + y = 32 + 64    

                2x = 96

                   x = 48 mile/hr

Substituting in eqn 2

                     48 + y = 64

                        y = 16 mile/hr  

Rate of the boat in still water  =  48 mile/hr

Rate of the current = 16 mile/hr