A motorboat travels 36km downstream in 2 hrs. In coming back upstream the trip takes 3 hrs. ?

Question

Find the rate of the boat in still water and the rate of the current?

Answer 1

let b = speed of boat in still water

     c = speed of current

remember... distance = rate x time (d = rt)

going downstream:

the boat travels 36 km, so d = 36

took 2 hours, so t = 2

since the current is helping your speed, r = b + c

so you have an equation:

36 = 2(b+c)

going upstream:

the boat travels 36 km, so d = 36

took 3 hours, so t = 3

since the current is NOT helping your speed, r = b - c

so you have an equation:

36 = 3(b-c)

you have two equations and two variables... now either use substitution or elimination to find that b = 15 km/hr and c = 3 km/hr.

Answer 2

We use the formula distance = rate * time. Let b = rate of the boat and c be the rate of the current. Then:

36 = 2(b + c)

36 = 3(b - c)

Simplify both equations and add together:

18 = b + c

12 = b - c

-----------------

30 = 2b

b = 15

18 = b + c

18 = 15 + c

c = 3

The boat travels at 15 km/h and the current is 3 km/h.