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
