The current in the lazy river is 2 mph. It travels 26 miles downstream in the same amount of time it takes to go 18 miles upstream. Find the speed of the boat i

Question

The current in the lazy river is 2 mph. It travels 26 miles downstream in the same amount of time it takes to go 18 miles upstream. Find the speed of the boat in still water.

Answer 1

Remember distance = rate times time or d=rt.

 

If the two trips take the same amount of time, then we can solve the equation for t, and set each equal to each other.  This allows you to solve them.

 

Downstream:  With current means you are going at a rate of x + 2 where x=still water speed.

Therefore,

26=(x+2)t or t = 26/(x+2)

 

Upstream:  Against current means you are going at a rate of x - 2

Therefore,

18=(x-2)t or t = 18/(x-2)

 

Setting these equal give the proportion:

 

26/(x+2) = 18/(x-2)

 

Solve by cross multiplication.

 

26(x-2)=18(x+2)

26x - 52 = 18x + 36

8x - 52 = 36

8x = 88

x = 11

 

The speed of the boat in still water is 11 mph.