Distance * Rate = Time

Question

A boat can travel 37 mph in still water. If it travels 135 miles with the current in the same length of time it travels 87 miles against the current, what is the speed of the current?

Answer 1

For this problem it helps to make a table of all the variables. The things we need to pay attention to are current speed, distance, rate, and time. It is also important to note that D=R*T

 

It is also important to note that with the current, the current speed C is added to the rate of the boat, and against the current it is subtracted. This makes sense because even if the boat engine is off, it will still be moving in the direction of the current at whatever speed the current is. 

 

So here is our table. We don't know time, but the trick here now is to note that the times equal each other as stated in the problem, and that if you rearrange D=R*T, you get T=D/R

 

variable....................D.........R........T

with current............135.....37+C.....D/R

against current........87......37-C.......D/R

 

Because the times are equal to each other, we can set the D/R of both with and against the current equal to each other. Doing so gives us: 135/(37+C)=87/(37-C)

 

Cross multiplying we get 135(37-C)=87(37+C)

Distributing gives us 4995-135C=3219+87C

Combining like terms gives us 222C=1776

Then finally dividing both sides gives us C=8 mph

 

We can check this by using T=D/R

For with the current, T=135/(37+8)=3

For against, T=87/(37-8)=3

 

The times equal each other, matching the criteria in the original problem.

Answer 2

Here's what we know:

D = r * t

135 = (37 + v)t

87 = (37 - v)t

 

135/t = 37 + v

87/t = 37 - v

 

By using the elimination method, we can get rid of that v variable:

222/t = 74

222 = 74t

222/74 = t

3 = t

 

So this is over three hours time.

135 = 3(37 + v)

45 = 37 + v

8 = v

 

Now to check:

87 = 3(37 - v)

29 = 37 - v

-8 = -v

8 = v

 

So the current's speed is 8 mph.