Please Help A boat traveled miles downstream in 1.5 hours. The return trip upstream took 2 hours. Find the boat’s rate if the rate of the current is 3 miles per hour.

Credit will only be earned for showing an algebra equation and solving it using algebra. Do not use the letter “x” in your equation. Use letter(s) that best describe the situation above.

Example 3.  Same time problem:  Upstream-Downstream.

First, let us explain the meaning of "upstream" and "downstream."

When a boat travels in the same direction as the current, we say that it is traveling downstream.

downstream

Thus if b is the speed of the boat in still water, and c is the speed of the current, then its total speed is

Downstream speed = b + c

When a boat travels against the current, it travels upstream.

upstream

In this case, its total speed is

Upstream speed = b − c

Problem.   The speed of a boat in still water is 30 mph.  It takes the same time for the boat to travel 5 miles upstream as it does to travel 10 miles downstream.  Find the speed of the current.

Solution.  The key to this type of problem is same time.  That will give the equation,

Time upstream = Time downstream

Now, speed, or velocity, is distance divided by time -- so many miles per hour:

v  =d

t

Therefore,

t  =d

v

The equation will be

 Time upstream=Time downstream

Distance upstream

Speed upstream  =Distance downstream

 Speed downstream

       Let x be the speed of the current.  Then according to the problem:

  _5_  

30 − x=    10    

30 + x

       Therefore,

5(30 + x)=10(30 − x)

150 + 5x=300 − 10x

5x + 10x=300 − 150

15x=150

x=10 mph

Step-by-step explanation: