the speed of a stream is 5mph. A boat travels 6 miles upstream in the same time

Question

the speed of a stream is 5mph. A boat travels 6 miles upstream in the same time it take 16 miles to travel downstream. What is the speed of the boat in the water still?

Answer 1

d=r*t

6=(r-5)*t

16=(r+5)*t

from 6=(r-5)*t we get t=6/(r-5)

substitute into the second equation

16=(r+5)(6/(r-5)

multiply both sides by (r-5)

16(r-5)=(r+5)*6

16r-80=6r+30

16r-6r=80+30

10r=110

r=11 mph is the speed of the boat

Answer 2

The trick to word problems is to extract what you know from the statement and use it to write equations.  Looking at the problem, we want to know the speed of the boat (V).   There are two statements about the speed of the boat and time (t).  The speed of the river(V_s) is mentioned and we will need it.  We will need to write equations in terms of the Speed and Time. 

 

One hint to keep from making mistakes:  Don put numbers into the variables until the very end.  That way, you won't get lost in the numbers and lose track of what they mean.

 

The boat travels upstream for some time and goes 6 miles.  The speed of the water river it down.

 (V-V_s)*t=6

 

Also, the boat travels downstream for the same time and goes 16 miles.  The speed of the river makes it go faster.

(V+V_s)*t=16

 

Both equations have V, V_s, and t.  We want "V", we know "V_s", and we don't care about "t" but will use it to find what we want.  Rearrange the two equations to solve for "t".

 

t=6/(V-Vs)

 

and

 

t=16/(V+Vs)

 

Because each one is solved for t, we can equate them.

 

t=   6/(V-Vs) = 16/(V+Vs)

 

Now, multiply both sides of the equation by (V-Vs)*(V+Vs).  After canceling, you will get:

 

6*(V+Vs) = 16*(V-Vs)

 

Expand the equation:

 

6V+6V_s = 16V-16V_s.

 

Rearrange to group the variables.

 

22V_s = 10 V

 

Get V all by itself and simplify

 

V=11Vs/5

 

Now you can put in the 5 mph stream velocity (V_s)

 

V=11*5/5 

 

V=11

 

The boat moves at 11 mph