Algebra word problem

Mathematics
Tutor: None Selected Time limit: 1 Day

A canoeist who took 6 hours to paddle 6 miles upstream was able to return to his starting spot in 45 minutes.  What was the rate of the current?

Apr 28th, 2015

Let x be the speed of the boat in still water.
Let y be the speed of the current of the river.
 
The boat's downstream speed relative to the river bank is x + y
The boat's upstream speed relative to the river bank is x - y

As the boat travels 6 miles downstream in 3 hours, we have
0.75(x+y)=6

0.75x + 0.75y = 6

x + y =  8(1)  
As the boat travels 6 miles upstream in 6 hours, we have
6(x-y)=6

6x - 6y = 6

x - y = 1 (2)

Using the elimination method for equations 1 and 2, we get

x + y = 8

                    +

x - y = 1


2x = 9

x = 9/2 =4.5


but x + y = 8

therefore, 4.5 + y = 8

y = 8 - 4.5 = 3.5


 
the rate of the current = y =3.5 miles/hour

Apr 28th, 2015

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