SOLUTION: A boat travels 30 km/h in still water. If this boat goes upstream in a river flowing at a rate of 12 km/h, for 5 km, and returns back downstream to its starting point, what is the

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Question 1208621: A boat travels 30 km/h in still water. If this boat goes upstream in a river flowing at a rate of 12 km/h, for 5 km, and returns back downstream to its starting point, what is the average speed for the whole trip in km/h?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52814) About Me  (Show Source):
You can put this solution on YOUR website!
.
A boat travels 30 km/h in still water. If this boat goes upstream in a river flowing at a rate of 12 km/h, for 5 km,
and returns back downstream to its starting point, what is the average speed for the whole trip in km/h?
~~~~~~~~~~~~~~~~~~~~~ 

The boat's own speed in still water  is 30 km/h.

The rate of the current in the river is 12 km/h.


So,  the boat' speed with the current (downstream)  is  u = 30 + 12 = 42 km/h;

     the boat' speed against the current (upstream) is   v = 30 - 12 = 18 km/h.


Now, if you know the theory, you may use the ready formula for the average speed of the two-ways trip


    V%5Baverage%5D = %282u%2Av%29%2F%28u%2Bv%29 = %282%2A42%2A18%29%2F%2842%2B18%29 = %282%2A42%2A18%29%2F60 = 2%2A42%2A%283%2F10%29 = 25.2 km/h.    ANSWER



        If you don't know this theory, 
        you may complete the solution in couple of steps.



The travel time upstream is   5%2F18  of an hour;  travel time downstream is  5%2F42  of an hour.


The average speed is  the total distance 5 + 5 = 10 km, divided by the total time  5%2F18 + 5%2F42  of an hour.


Thus the average speed is


    10%2F%285%2F18%2B5%2F42%29 = 10%2F%28%28%285%2A42%2B5%2A18%29%2F%2818%2A42%29%29%29 = %2810%2A%2818%2A42%29%29%2F%285%2A42%2B5%2A18%29 = %282%2A18%2A42%29%2F%2842%2B18%29 = the same formula and the seme result = 25.2 km/h.


ANSWER.  The average speed of the two-ways trip is 25.2 km.h

Solved.



Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


Here is a different way to get to the average speed.

The upstream speed is 30-12 = 18 km/h; the downstream speed is 30+12 = 42 km/h.

The ratio of the two speeds is 18:42 = 3:7. Since the distances are the same, the ratio of the times at the two speeds is 7:3. So the average speed is

%287%2F10%29%2818%29%2B%283%2F10%29%2842%29=126%2F10%2B126%2F10=252%2F10=25.2

ANSWER: 25.2