Harry has to go 32 miles with the wind current on his Firebolt accross the Quidditch field where the wind current is 4 mph, then back the same distance to the starting point. If the wind travel was done in 3 hours and 20 minutes, at what speed was the broom gliding then?

Question

anonymous · Answer

$$
\frac{32}{x+4}+\frac{32}{x-4}=\frac{10}{3}\
\frac{64x}{x^2-16}=\frac{10}{3}\
\frac{10x^2}{3}-64x-\frac{160}{3}=0\
x=20
$$

anonymous · Answer

Doublecheck: If he's going 20 mph, then with the wind he's going 24 and makes it there in 1 1/3 hrs, and on the way back against the wind he's going 16 and makes it in 2 hrs, added for a total of 3 1/3 hrs (3hrs 20 min)

lgbasallote · Answer

hmm clever =_=