Distance, rate, time word problem.

Question

A boat travels 36km downstream in 2 hours.  The return trip takes 3 hours.  What is the rate of the current??

Answer 1

first, identify the quantities involved

let c be the rate of the current

let b be the rate of the boat

 

second, write the formulas that relate these numbers

d=rt is the general formula for distance, rate, time problems

 

When the boat travels downstream, its rate is (b + c)

when the boat travels upstream, its rate is (b - c)

 

36 = (b+c)*2

36 = (b-c)*3

 

Solve these for b and c, and you'll have c.

Answer 2

Let x = speed of boat in still water

     y = speed of current

 

Speed upstream (against current) = x-y

Speed downstream (with current) = x+y

 

Distance = (rate)(time)

 

2(x+y) = 36

3(x-y) = 36

 

So, x+y = 18

      x-y = 12

 

2x = 30     x = 15 km per hr

                y =   3 km per hour