Finding current and rate of boat in still water.

Question

A boat can travel 24 miles in 3 hours when traveling with a current. Against the same current, it can travel only 16 miles in 4 hours. Find the rate of the current and the rate of the boat in still water.

Answer 1

Let speed of boat in still water = x mph

& speed of current or stream = y mph

Downstream speed  =  x + y

Upstream speed      =  x - y

Using the relation , distance = speed x time, we get,

3(x + y) = 24 or, x + y =8

4(x - y)  = 16 or, x - y  =4

Solving the system of equations simultaneously, we get,

x = 6, y= 2

Rate of current = 2 mph, rate of boat in still water = 6 mph.......Answered.

Answer 2

Let "b" represent speed of boat in still water

Let "c" represent speed of current

Let "t" represent time

 

Downstream(same direction) =(b+c)*t

Upstream(against current)=(b-c)*t

 

(b+c)*3=24

(b-c)*4=16

 

3b+3c=24....all sides can be divided by 3 =b+c=8

4b-4c=16.....all sides can be divided by 4 =b-c=4

 

Use Elimination method

 

b+c=8

b-c= 4 Subtracting 

=====

 2c=4

find c by dividing both sides by 2. c=2

 

if c=2, substitute to get b

b+2=8

  -2=-2

======

b=6

 

Speed of boat in still water =6mph

rate of current=2mph