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

Studypool's Notebank makes it easy to buy and sell old notes, study guides, reviews, etc.
Click to visit
The Notebank
...
Apr 28th, 2015
...
Apr 28th, 2015
Mar 27th, 2017
check_circle
Mark as Final Answer
check_circle
Unmark as Final Answer
check_circle
Final Answer

Secure Information

Content will be erased after question is completed.

check_circle
Final Answer