Would this make for a good high school algebra problem?

High school algebra problems tend not to be very interesting. I thought that this common recreational math problem given to children might provide for some interest.

A frog is at the bottom of a 30 foot well. The frog climbs 5 feet per day and then goes back down 4 feet every night. How long does it take the frog to escape the well.

The common response to this is 30 days, one foot each day. Algebraically, the distance d at the end of t days is d = (5–4)t, which gives t = d. For d = 30, t = 30. What is wrong with this reasoning and how can the algebra be corrected to answer this and similar problems?