algebra word problem, a motorboat travels 135 mi....

Question

A motorboat travels
135mi
in
5
hours going upstream. It travels
195mi
going downstream in the same amount of time. What is the rate of the boat in still water and what is the rate of the current?

Answer 1

v = speed in still water

 

c = speed of current

 

velocity * time = distance

 

Upstream:

 

(v - c) (5) = 135

 

Downstream:

 

(v + c) (5) = 195

 

Just solve a system of 2 equations in 2 unknowns v and c.

 

5v - 5c = 135

5v + 5c = 195

 

Divide both equations by 5 to simplify.

 

v - c = 27

v + c = 39

 

Get v = 27 + c from top equation and substitute in bottom equation.

 

(27 + c) + c = 39

 

Then

 

c = (39 - 27) / 2 = 6

 

v = 27 + c = 27 + 6 = 33

 

Speed in still water is 33 mph

Speed of current is 6 mph

Answer 2

Just a note, following Arturo's fine solution:

 

Once you get to:

 

v - c = 27

v + c = 39

 

perhaps an even more direct way to the answer is the addition method; just add the left and right sides together.

 

v - c  = 27

v + c = 39

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

2v+0 = 66 --> 2v = 66 --> v = 33

 

Then you can solve for c with either equation, as before.

 

Just another possibility that is sometimes a little more direct.  But the above solution equally good.