application of rational equations

Question

The speed of the current in a river is 22 miles per hour. A boat travels 99 miles downstream (with the current) in this river in the same time that it travels 55 miles upstream (against the current). Find the speed of the boat in still water.

Answer 1

So let x be the speed of the boat in still water, that makes the speed with the current x+22 and against the current x-22.

Now use the standard motion problem chart involving rate*time=distance.

 

                            rate                      time                  distance

downstream           x+22                    99/(x+22)           99

upstream               x-22                     55/(x-22)            55

 

Since the problem says it took the same amount of time to go 99 miles as it did 55 miles, the times above must be equal.

 

So 99/(x+22) = 55/(x-22)

 

In this particular problem, you can just cross multiply to get

99(x-22) = 55(x+22)

99x - 2178 = 55x + 1210

44x            = 3388

x               =  77

 

So the boat can travel 77 miles per hour in still water.

 

Hope this helped.