SOLUTION: A boat travels 20 km/h in still water. If this boat goes upstream in a river flowing at a rate of 6 km/h for 10 km, and then returns back downstream to its starting point, what is

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Question 1185907: A boat travels 20 km/h in still water. If this boat goes upstream in a river flowing at a rate of 6 km/h for 10 km, and then returns back downstream to its starting point, what is the average speed for the whole trip in km/h?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Upstream
10%2F%2820-6%29
10%2F14
5%2F7hours

Downstream
10%2F%2820%2B6%29
10%2F26
5%2F13hours

Average speed of whole round-trip:
%2810%2B10%29%2F%285%2F7%2B5%2F13%29 kilometers
Simplify and compute.



-----------------------------------------
----------------------------------------- 

              SPEEDS         TIMES               DISTANCES

upstream        20-6         10/(20-6)                10

downstream      20+6         10/(20+6)                10

TOTALS                     10/(20-6)+10/(20+6)       2*10

Average Speed, round-trip
%282%2A10%29%2F%2810%2F%2820-6%29%2B10%2F%2820%2B6%29%29

%2810%2F10%29%282%2F%281%2F%2820-6%29%2B1%2F%2820%2B6%29%29%29

highlight_green%282%2F%281%2F%2820-6%29%2B1%2F%2820%2B6%29%29%29---------------compute the value.

Answer by ikleyn(52787) About Me  (Show Source):
You can put this solution on YOUR website!
.
A boat travels 20 km/h in still water. If this boat goes upstream in a river flowing at a rate of 6 km/h for 10 km,
and then returns back downstream to its starting point, what is the average speed for the whole trip in km/h?
~~~~~~~~~~~~~~~~~ 

The speed upstream   is   u = 20-6 = 14 km/h


The speed downstream is   v = 20+6 = 26 km/h.


The average speed of the whole roundtrip is  %282uv%29%2F%28u%2Bv%29 = %282%2A14%2A26%29%2F%2814%2B26%29 = 18.2 km/h.    ANSWER

Solved.


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The key of my solution is to use the formula   %282uv%29%2F%28u%2Bv%29   for the average speed of the whole roundtrip.


Also notice,  that this formula and the answer  DO  NOT  DEPEND  on the length of the trip:   for example,
if the length is  40  kilometers in each of the two directions (instead of 10 kilometers in your problem),
the answer for the average speed of the roundtrip will be the same.


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For your education,  see the lessons
    - Calculating an average speed: a train going from A to B and back
    - One more problem on calculating an average speed
in this site.