Your first guess was probably 22 minutes.  Would you believe the answer is 40 minutes?

Why? With the wind behind her, her speed increases by 60 percent (to 160/100). Against the wind, it decreases by 60 percent (to 40/100). If her speed on a calm day is 100 percent, we're comparing 160 percent speed with the wind (the 10 min journey) against 40 percent speed into the wind.  So it takes 4 times longer than the 10 minute journey.

Still unsure? Ask a maths teacher!