Awoman can bicycle 27 miles in the same time it takes her to walk 9 miles. she can ride 10 mph faster than she can walk. how fast can she walk

 Let the time be t.  We don't necessarily need to find the elapsed time, but do need to find her usual walking speed.

Recall that distance = (rate)(time)

Walking speed = s

driving speed = s + 10  (mph)
               
                27 mi                 9 mi   
Then t = =
               (s+10) mph         s mp

This equation has only one variable, s.  We can solve it for s as follows:

( 27 mi) * (s ) = (9 mi)(s)+ 90 (mi)(mph)

27s = 9s + 90, or 18 s = 90, or s = 90/18 = 10/2 = 5.  Her walking speed is 5 mph.  Her riding speed is 5+10 mph, or 15 mph.

Both 5 mph and 15 mph sound reasonable, don't they?  5 mph on foot and 15 on the bike.