October 2016
Problem of the Month

Against the Wind
by Sam Loyd

A cyclist rode a mile on her bicycle in three minutes with the wind, and returned in four minutes against the wind.

Assuming that at all times she applies the same force to the pedals, how long would it take her to ride a mile if there were no wind?

Show your work!

Solution to the Problem:

It would take the cyclist 3 3/7 minutes (24/7 minutes) to ride a mile with no wind.

Let x = the speed of the cyclist with no wind.
Let y = the speed of the wind.
Then x + y = 1/3 mile/min
and x - y = 1/4 mile/min

Solving for x, add the two equations to obtain:
2x = 1/3 + 1/4
So, 2x = 7/12 or
x = 7/24 miles per min.

That means that she can ride 7 miles in 24 minutes or 1 mile in 24/7 minutes.

Correctly solved by:

1. Kimberly Howe	Vienna, Virginia
2. James Alarie	Flint, Michigan
3. Olivia Edwards	Park Ridge, Illinois
4. Keegan Genzer	Mountain View High School, Mountain View, Wyoming
5. Tom Laidlaw	Vancouver, Washington

Send any comments or questions to: David Pleacher