Let the uphill speed be 2x and the downhill speed be 3x.

at school

2/5 is uphill, so the uphill time is (2/5)/(2x).

3/5 is downhill, so the downhill time is (3/5)/(3x).

So time is

(2/5)/(2x)+(3/5)/(3x)=36

1/(5x)+ 1/(5x)=36

2/(5x)=36

5x= 1/ 18

x= 1/90

When I got home, I turned the mountain upside down.

3/5 is uphill, so the uphill time is (3/5)/(2x)=27.

2/5 is downhill, so downhill time is (2/5)/(3x)= 12.

So it takes 27+ 12=39 minutes.