Lupe can ride her bike at a rate of 20 mph when there is no wind. on one particular day, she rode 2 miles against the wind and noticed that it took her the same amount of time as it did to ride 3 miles with the wind. how fast was the wind blowing that day? 4 mph 7 mph 10 mph 12 mph

Let wind speed = x mph 

when she rode 2 miles against the wind we have:-
speed = distance / time so
20 - x  = 2 / t (1)      where t is the time she took.

when riding with the wind we have 

20 + x = 3 / t(2)   adding equations (1) and (2):-

40  =  2/t + 3/t
40 =  5/t
t = 5/40 = 1/8 hr 

x = 20 - 2 / 1/8  = 20 - 16 = 4

Wind speed was 4 mph Answer

Hello there! Your answer should be 4 mph. Reasoning:
2 = (20 - x) * t 
3 = (20 + x ) * t 
Time is the same for both equations. Solve for T.
2/(20-x) = 3/(20+x)
the answer is 4 mph.
Please tell me if I was right!