SOLUTION: A motorboat travels 156 kilometers in 6 hours going upstream. It travels 252 kilometers going downstream in the same amount of time. What is the rate of the boat in still water and

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Question 1154291: A motorboat travels 156 kilometers in 6 hours going upstream. It travels 252 kilometers going downstream in the same amount of time. What is the rate of the boat in still water and what is the rate of the current?
Found 2 solutions by greenestamps, josgarithmetic:
Answer by greenestamps(13198)   (Show Source): You can put this solution on YOUR website!


The upstream speed (boat speed minus current speed) is 156/6 = 26km/h.

The downstream speed (boat speed plus current speed) is 252/6 - 42km/h.

Now you have a situation encountered in a wide range of problems -- a second number added to a first number gives 42 while the second number subtracted from the first gives 26.

If you picture those operations on a number line, a logical conclusion is that the first number is halfway between 26 and 42, and then the second number is the difference between that number and either of 26 or 42. So...

boat speed = (26+42)/2 = 34
current speed = 42-34 = 8 or 34-26 = 8

ANSWERS:
boat speed 34km/h
current speed 8km/h

Of course, after you find the upstream and downstream speeds you can find the boat speed and current speed with formal algebra:

b+c = 42
b-c = 26
--------
2b = 68
b = 34
c = 42-34 = 8

However, if formal algebra is not required, the shortcut to the final answers is a very useful one, since it occurs in a wide range of different types of problems.
Answer by josgarithmetic(39616)   (Show Source): You can put this solution on YOUR website!
U=156 kilometers
D=252 kilometers
T=6 hours
r, unknown boat speed in still water
c, unknown speed of the stream 
            SPEED       TIME       DISTANCE

UP             r-c       T            U

DOWN           r+c       T            D


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