Math PSAT Help?

Question

Hey I'm studying for PSAT's from the Princeton Review book and this question has really got me?

Michelle rode her bicycle from her house to school at an average speed of 8 miles per hour. Later that day, she rode from school back home along the same route at an average speed of 12 miles per hour. If the round trip took her 1 hour, how many miles long is the round trip?

The answer is 9 and 3/5 or 48/5 but can you tell me how to get it?

Answer 1

let the time to go be t
let the time to return be 1 - t

distance going = distance returning
d = d
(but distance = rate x time) so substituting rate x time for d

(rate x time) going = (rate x time) returning

8 x t = 12 x (1 - t)
8t = 12 -12t

20t = 12
t = 12/20 or 3/5


but d = r x t so d = 3/5 x 8 = 24/5 or 4 4/5

so the round trip wil be 2 x 24/5 = 48/5 or 9 3/5

Answer 2

d= distance and distance/ rate = time, so:
d/8 +d/12 = 1
3d/24 + 2d/24 = 1
5d= 24
d = 24/5 = 1-way distance
2d = 48/5 = round trip distance