two dists

the time to travel from A->B = 3 hours
Going from B->A has the same distance, but time of 3 and half hours
you travel downhill at 75 mph
over flat terrain at 60 mph
and travel uphill at 50 mph
the road is the same road each way


So there are two different time functions..?

lets use a simple example

we have 10 mile walk. i can walk 5mph uphill and 7.5mph downhill.
the walk is totally up or downhill.
it would be 2 hours to walk up the hill
but only 1 hour and 20 minutes down the hill

We can probably model the difference between the two equations
Let t1 and t2 represent times to walk uphill or downhill
remember the speed = distance over time
so time = distance over speed
t1 = d/5, t2 = d/7.5

if we know what t1 and t2 are, we can find out what d is
and vice versa

as distance = time multiplied by speed
d = t1*5 = t2*7.5
replace t1 and t2 with actual numbers
d = 2*5 = 1*7.5 + 1/3*7.5
d = 10 = 10
:)


now lets tackle the previous fight

it takes 3 hours to travel from A to B
but 3 and a half hours to travel back the same road

going uphill averages 50 mph
on flat terrain averages 60mph
and going downhill averages 75 mph

Let t1 represent A to B, t2 represent B to A
time = distance over speed
There will be 3 different distances, one for each terrain
d1 : uphill, d2 : flat, d3 : downhill
for t2, just flip down and up
3.0 = d1 / 50 + d2 / 60 + d3 / 75
3.5 = d1 / 75 + d2 / 60 + d3 / 50

we can get d1 by multiplying both sides by its divisor

150.0 = d1 + 50d2/60 + 50d3/75

subtract 50d2/60 + 50d3/75 from both sides
d1 = 150.0 - 50d2/60 + 50d3/75
Simplify terms
d1 = 150.0 - 5d2/6 + 2d3/3

we can do the same for the second distance
3.5 = d1 / 75 + d2 / 60 + d3 / 50 maybe?

screw that
im just going to start doing distance = time multiplied by speed
let big D represent distance.. its made of smaller distances
D = d1 + d2 + d3
...
im stuck at how to make the equations
i feel like this should work but idk what to do now