Time at home is 8 minutes less than school time, that is, 8/60 hours less.

It's one kilometer from home to school. Then the school time is: (a/5+a/ 15) hours.

The time to go home is: (a/5+a/ 15-8/60) hours.

When I go home, take the bus13. The distance is13 (A/5+A/15-8/60) and take the bus15.

2/3 walk, the walking distance is: 2/3(a/5+a/ 15-8/60) times 5.

Then the distance from home to school is:1/3 (a/5+a/15-8/60) times15+2/3 (a/5+a/15-8/60) times.

Finally a=5, then the distance from home to school is 10 km.

Check that the school time is: (a/5+a/ 15) class hours =3/4 class hours.

The time to go home is: 3/4-8/60=6/5 hours.

Take the bus 1/3, and the distance is: 1/3(6/5) times15 = 6km.

2/3 walk, the walking distance is: 2/3(6/5) times 5=4 kilometers.

The whole journey is 6+4= 10 km.

So: the answer is correct.