document.write( "Question 275984: a cyclist travels 30mi in 3 hours going against the wind and 80mi in 5 hours with wind. What is the rate of the cyclist in still air and what is the rate of the wind? \n" ); document.write( "

Algebra.Com's Answer #854106 by greenestamps(13326) $\"\"$ $\"About$

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\n" ); document.write( "These kinds of problems are intended as mathematical exercises, without concern for the physics.

\n" ); document.write( "In this problem, the speed of the cyclist against the wind is 30/3 = 10 mph and with the wind is 80/5 = 16 mph.

\n" ); document.write( "You can solve the problem using formal algebra:
\n" ); document.write( "c the speed of the cyclist in still air
\n" ); document.write( "w the speed of the wind
\n" ); document.write( "c+w=16; c-w=10 --> c=13, w=3

\n" ); document.write( "But an informal solution using logical reasoning is much easier: the speed of the cyclist is halfway between his speed with the wind and his speed against the wind:
\n" ); document.write( "(10+16)/2 = 13
\n" ); document.write( "and the speed of the wind is the difference between that speed and either of the other speeds:
\n" ); document.write( "16-13 = 3 mph, or 13-10 = 3 mph

\n" ); document.write( "ANSWERS: cyclist 13 mph; wind 3 mph

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