Rate distance time

Question

The speed of a boat in still water is 7 miles per hour. If the boat travels 3 miles downstream in the same amount of time it takes to travel 2.5 miles upstream, what is the speed of the current?

Answer 1

For this we use the basic formula

distance = rate * time

d = rt

 

Rearrange your equation to solve for time:

t = d/r

 

Going downstream your rate, or speed, is

the speed of the boat added to the speed of the water:

r = 7 + s     where s represents the speed of the stream

 

Downstream we have:

t = 3/(7+s)

 

Going upstream your rate, or speed, is

the speed of the boat minus the speed of the stream

r = 7-s

 

Upstream we have:

t = 2.5/(7-s)

 

Since your times are equal set the two equations

equal to each other and solve for s

 

3/(7+s) = 2.5/(7-s)

Cross multiply

3(7-s) = 2.5(7+s)

multiply through your parenthesis

21-3s = 17.5 + 2.5s

Add 3s to both sides

21 = 17.5 + 5.5s

Subtract 17.5 from both sides

3.5 = 5.5s

Divide both sides by 5.5

 

3.5/5.5 = s

 

This doesn't come out to a very pretty decimal so

let's convert 3.5 and 5.5 to improper fractions

 

s = (3 1/2)/(5 1/2)

s = (7/2)/(11/2)

s = (7/2)(2/11)

s = 7/11 mph

 

Note:  3.5/5.5 = 0.636363...

                            __

                      = 0.63

 

You could round that to 0.64 mph if you need a decimal answer