algebra with distance

Question

A small motorboat went downstream a distance of 36km in 3 hours but took 4 hours to return back against the current. What was the speed of the boat in still water and the speed of the current?

Answer 1

distance = rate*time  ...   d = rt

Let b = speed of boat

Let c = speed of current

 

Downstream:  36 = 3(b+c)

Upstream:      36 = 4(b-c)

 

3b + 3c = 36  {equation 1}

4b - 4c = 36   {equation 2}

 

multiply equation 1 by 4

multiply equation 2 by 3

add equations and solve for b

 

12b + 12c = 144

12b - 12c = 108

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

24b = 252

 

b = 10.5 km/hr

 

substitute that back into equation 1:

3(10.5) + 3c = 36

31.5 + 3c = 36

3c = 4.5

c = 1.5 km/hr

 

The speed of the boat is 10.5 km/hr

The speed of the current is 1.5 km/hr