Systems: Cyclist Speed
A cyclist can cover 1 mile in 3 minutes when the wind assists him and takes 4 minutes when riding against the wind. How long would it take him to travel the same distance if there's no wind?
Answer
Let $x$ denote the speed of the cyclist and let $w$ denote the wind speed. When going with the wind,
\[
x + w = \frac{1}{3}
\quad (\text{miles/min}).
\]
When going against the wind,
\[
x - w = \frac{1}{4}.
\]
Adding these equations yields \(2x = \tfrac{1}{3} + \tfrac{1}{4} = \tfrac{7}{12}\), so \(x = \tfrac{7}{24}\). Thus, in still air, it takes \(\displaystyle \frac{1}{x} = \frac{24}{7} \approx 3.43\) minutes to bike 1 mile.