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Did You Figure it Out? Get the Answer to the Riddle from E-News Issue No. 1, February 2019

2019-02-12

Boat Trip

e-news, newsletter, riddle, boat trip
How long would Lena be on the water?

On a hot and sunny summer day, Lena decides to take a trip with her boat. It takes 5 hours for her to row her boat down the river. If she continues to row at the same pace, she will need 6 hours to row back up the river. Now imagine that Lena is traveling the same distance with her boat on a lake (without a current).

How long would she be on the water if her boat traveled at a constant speed?


Solution

It is a uniform motion, so the following physical relationship is valid:

Speed x time = distance   or   s ∙ t = d

The time t” is calculated accordingly:   t = d/s

For our example this means:

5 = d/(S + s) → 5(S + s) = d, and

6 = d/(S - s) → 6(S - s) = d   

Where “S” the speed of the boat and “s” is the speed of the current.                                                      

By setting the two equal to one another, you get:

5(S + s) = 6(S - s)

5S + 5s = 6S - 6s

11s = S                  

So, the speed of the boat is eleven times greater than the speed of the current.

t = d/s and the distance d” can be calculated using

d 5(S + s) = 6(S - s),

which yields d = 5 [ S + (1/11)S ] = 6 [ S - (1/11)S ] = (60/11)S

and therefore

t = d/s = 60/11

Because you have to consider the distance there and back, the result is:

t = 120/11 = 10 (10/11)h = 10h 54,5 seconds

It is logical that a trip without a current is shorter, because traveling with the current is shorter than traveling against the current.


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