avg. speed in km/h = distance / time
t: time
d: distance
NOTphysicsnerd: He drives at a constant speed of 90.0km/h except for a 30 minute rest stop.
t * 90km/h = d
NOTphysicsnerd: His average speed for the trip is 78 km/h.
avg speed = d / (t + 30min) = 78km/h
equations:
t * 90 = d
d / (t + 0.5) = 78
[input]solve( t * 90 = d, d / (t + 0.5) = 78 )[/input]
or solve on paper..
d / (t + 0.5) = 78
=> d = 78 * (t+0.5)
t * 90 = d = 78 * (t+0.5)
t * 90 = 78*t + 78/2
t * 90 - 78*t = 78/2
t * (90 -78) = 39
t * 12 = 39
t = 39/12 = 13/4 = 3.25 =>
d = 13/4*90 = 292.5 result check:
[input]3.25hour*90km/h in km[/input]
[input]292.5km/78km/h-30min in std[/input]
NOTphysicsnerd: a: How much time does the whole trip take?
t = 3.25hours = 3hours + 15minutes
NOTphysicsnerd: b: How far does Caleb travel?
d = 292.5km
+3146 
