Question

A bicyclist travels at a constant rate on her bicycle. Biking with the wind, it takes 2.6 hours to travel 52 miles. Biking against the wind, the return trip takes 4 hours. If there is no wind, how fast was the cyclist biking?
(step by step help, I tried it multiple times but got lost and confused completely)

Answer 1

you are looking for the rate yes?

Answer 2

yes

Answer 3

one way is to use distance equals rate time time
the rate going is \(r+w\) and the rate returning is \(r-w\)
then \[52=(r+w)\times 2.6\] and
\[52=(r-w)\times4\]

Answer 4

where \(r\) is the rate you are looking for and \(w\) is the rate of the wind

Answer 5

ok but then how do I solve it from there?