What is the speed?

Question

The speed of a stream is 5 mph. If a boat travels 46 miles downstream in the same time that it takes to travel 23 miles upstream, what is the speed of the boat in still water?

Answer 1

Good evening! This is commonly referred to as a "dirt" problem. D=rt (distance =rate times time). Since the time is the same, rearranging the equation we get t=D/r, so the distance upstream divided by the rate is equal to the distance downstream divided by the rate. The rate downstream is the rate in still water plus the stream flow while the rate upstream is the rate in still water minus the stream flow.

 

Therefore:

 

46/(x+5) =23/(x-5)

 

cross multiplying gives you

 

46(x-5) = 23(x+5)

 

Distributing gets you

 

46x - 230 = 23x + 115

 

Combine like terms

 

46x-23x = 115+230

 

Simplify

 

23x = 345

 

Divide by 23

 

x = 15

 

So the speed of the boat in still water is 15 mph

 

Hope this helps

 

Mike

Answer 2

"Story Problem" posted by Allison is somewhat similar and may help.