6.75 miles. I wrote this down, took it home, worked it out, took a picture of my work, but this morning I forgot to bring my phone to work. Essentially, it's basic math.

Assuming:

1.5 m/h up hill

4.5 m/h down hill

6hour total trip

So let x equal the time it takes to go up the mountain

and y equal the time it takes to go back down the mountain

x + y = 6 hours

Getting our equations and finding the distance:

1.5 m/h * x h = distance to the top of the mountain

4.5m/h * y h = distance down

Assuming Jack took the same path up and down

1.5 m/h * x h = 4.5 m/h y * h

Solve for x and y and plug in the variables:

y = 3/x

x = 3y

x + y = 6 hours or 3y + y = 6 hours

y = 4/6 hours or 1.5 hours

4.5 m/h * y hours = distance

4.5 m/h * 1.5 hours = 6.75 miles