# Another river current puzzler

**URL:** <https://community.cartalk.com/t/another-river-current-puzzler/72750>\
**Category:** The Show\
**Created:** [May 30, 2012, 8:35pm UTC](https://community.cartalk.com/t/another-river-current-puzzler/72750 "2012-05-30T20:35:53Z")\
**Posts on this page:** 8\
**Page:** 1

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**Author:** ![Mechaniker](https://avatars.discourse-cdn.com/v4/letter/m/13edae/32.png) [@Mechaniker](https://community.cartalk.com/u/Mechaniker)\
**Post date:** [May 30, 2012, 8:35pm UTC](https://community.cartalk.com/t/another-river-current-puzzler/72750/1 "2012-05-30T20:35:53Z")

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Two men, both with rowing speeds of 5 mph in still water, start out rowing on a river at the same time in the morning. Man A rows upstream from point A to point B, while man B rows downstream from point B to point A. They pass each other at noon on the river and continue rowing. Man B, rowing downstream, reaches point A at 4 in the afternoon. Man A, rowing upstream, reaches point B at 9 in the evening.

How fast is the river current?

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**Author:** ![missileman](https://sea1.discourse-cdn.com/cartalk/user_avatar/community.cartalk.com/missileman/32/1366_2.png) [@missileman](https://community.cartalk.com/u/missileman)\
**Post date:** [May 30, 2012, 11:43pm UTC](https://community.cartalk.com/t/another-river-current-puzzler/72750/2 "2012-05-30T23:43:43Z")

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Just fast enough to get the results as they were stated. Sorry…I have a young relative visiting and that’s her answer. She wanted to see it in print.

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**Author:** ![hybrid314](https://avatars.discourse-cdn.com/v4/letter/h/bb73d2/32.png) [@hybrid314](https://community.cartalk.com/u/hybrid314)\
**Post date:** [June 6, 2012, 5:42am UTC](https://community.cartalk.com/t/another-river-current-puzzler/72750/3 "2012-06-06T05:42:28Z")

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Too fast for my speed. I ended up with a quadratic equation with imaginary roots. I assume algebra is required to solve this one, unless I missed something.

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**Author:** ![George\_San\_Jose1](https://avatars.discourse-cdn.com/v4/letter/g/e5b9ba/32.png) [@George\_San\_Jose1](https://community.cartalk.com/u/George_San_Jose1)\
**Post date:** [June 6, 2012, 6:36am UTC](https://community.cartalk.com/t/another-river-current-puzzler/72750/4 "2012-06-06T06:36:11Z")

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Maybe the only _imagined_ they passed each other then 😉

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<div class="post-metadata">

**Author:** ![Mechaniker](https://avatars.discourse-cdn.com/v4/letter/m/13edae/32.png) [@Mechaniker](https://community.cartalk.com/u/Mechaniker)\
**Post date:** [June 6, 2012, 7:08am UTC](https://community.cartalk.com/t/another-river-current-puzzler/72750/5 "2012-06-06T07:08:48Z")

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# _" I assume algebra is required to solve this one, unless I missed something."_

Only linear algebra, nothing more.

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**Author:** ![jesmed1](https://sea1.discourse-cdn.com/cartalk/user_avatar/community.cartalk.com/jesmed1/32/2097_2.png) [@jesmed1](https://community.cartalk.com/u/jesmed1)\
**Post date:** [June 6, 2012, 7:54am UTC](https://community.cartalk.com/t/another-river-current-puzzler/72750/6 "2012-06-06T07:54:15Z")

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Current speed = 1 mph.

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<div class="post-metadata">

**Author:** ![Mechaniker](https://avatars.discourse-cdn.com/v4/letter/m/13edae/32.png) [@Mechaniker](https://community.cartalk.com/u/Mechaniker)\
**Post date:** [June 6, 2012, 8:03am UTC](https://community.cartalk.com/t/another-river-current-puzzler/72750/7 "2012-06-06T08:03:33Z")

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# _“Current speed = 1 mph.”_

You are correct !!!

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<div class="post-metadata">

**Author:** ![jesmed1](https://sea1.discourse-cdn.com/cartalk/user_avatar/community.cartalk.com/jesmed1/32/2097_2.png) [@jesmed1](https://community.cartalk.com/u/jesmed1)\
**Post date:** [June 6, 2012, 8:13am UTC](https://community.cartalk.com/t/another-river-current-puzzler/72750/8 "2012-06-06T08:13:46Z")

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let D1 be distance from A to point at which boats meet  
let D2 be distance from B to point at which boats meets  
let Vdown be speed of boat going downstream  
let Vup be speed up boat going upstream  
let X be speed of current  
let T1 be elapsed time between departure and meeting at noon

For first part of the trip (until noon):  
T1 = D1/Vup = D2/Vdown

For second part of trip ( after meeting at noon until finish):  
D1 = Vdown x 4 hrs  
D2 = Vup x 9 hrs

Combining above eqns:  
4Vdown/Vup = 9Vup/Vdown

Cross multiply:  
4Vdown(squared) = 9Vup(squared)

Since still water speed of both boats is 5 mph, relative to fixed points A and B,  
Vup = 5-X  
Vdown = 5+x

Substitute into the equatioin with the Vsquareds:  
4(5+x)(squared) = 9(5-x)(squared)

expand and solve for x.  
or just trial and error.

x=1