SOLUTION: It takes 5 hours for a boat to travel 80 miles downstream. The boat can travel the same distance back upstream in 8 hours. Find the speed of the boat in still water and the speed o

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Question 1129303: It takes 5 hours for a boat to travel 80 miles downstream. The boat can travel the same distance back upstream in 8 hours. Find the speed of the boat in still water and the speed of the current.
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
Against the current the effective speed (the speed relative to the river bank) is


u - v =  = 10  miles per hour.     (1)   (u = the speed of the boat in still water;  v = the speed of the current)



With the current, the effective speed is

u + v =  =  16 miles per hour.     (2)



Add equations (1) and (2)


2u = 16 + 10 = 26  ====>  u = 26/2 = 13 mph is the speed of the boat in still water.    ANSWER



Subtract eq(1) from eq(2)

2v = 16 - 10 = 6  ====>  v = 6/2 = 3 mph  is the speed of the current.     ANSWER

Solved.


The lesson to learn from this solution and the tnings to memorize are : 

    1.  The effective speed of a boat traveling with    a current is the sum        of the two speeds.

    2.  The effective speed of a boat traveling against a current is the difference of the two speeds.

    3.  It gives a system of two equations in two unknowns, which fits very well for solving by the elimination method.



Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


There are so many types of problems like this that it might be worthwhile to look at a quick way to solve them without formal algebra... if, of course, a formal algebraic solution is not required.

You have a downstream speed of 80/5 = 16mph, which is the speed of the current added to the speed of the boat; you have an upstream speed of 80/8 = 10mph, which is the speed of the current subtracted from the speed of the boat.

Common sense (or a bit of visualization on a number line) says that the speed of the boat is halfway between those two speeds; and then the speed of the current is the difference between the speed of the boat and either the upstream or downstream speed.

In this problem....

The boat's speed is (16+10)/2 = 13mph;
The speed of the current is 16-13 = 3mph (or 13-10 = 3mph).

You are doing exactly the same calculations as with formal algebra; but you aren't slowed down by writing and solving equations.
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