# TADM2E 1.3

a ----------- c ----------- b

\ / \--------- d ---------- /

If the distance from *a* to *b* going through *d* is less than the distance from *a* to *b* going through *c* but there is a busy traffic intersection at *d* with a stop sign that is always backed up, then the route from *a* to *b* through *c* is faster, but the route through *d* is shorter.

For example,

$ dist(a, c) = 10 $ miles

$ dist(c, b) = 5 $ miles

So the distance from *a* to *b* through *c* is 15 miles. Assuming you drive 30 miles per hour, the time to travel this would be 30 minutes

$ dist(a, d) = 5 $ miles

$ dist(c, b) = 5 $ miles

So the distance from *a* to *b* through *d* is 10 miles. Assuming you drive 30 miles per hour, the time to travel this would be 20 minutes, but due to the busy intersection at *d*, you are delayed 15 minutes, the total time would be 35 minutes.