Question

A person takes a trip, driving with a constant speed 85.6 km/h except for a 22.6 minute rest stop.
If the person's average speed is 61.6 km/h, how far is the trip? Answer in units of km.

Answer 1

Let T be the total time (in hours) and X be the distance (in km). 22.6 minutes is 0.3767 hours. You can write two equations in the two unknowns:
X = 61.6 T (using the average speed)
and
X = 85.6 (T-.03767)
(using the time spent actually driving)
This means that
61.6 T = 85.6 T - 32.24
24.0 T = 32.24
T = 1.343 h
Now solve for X
X = ?

Answer 2

22.6 minutes is 22.6/60 hours = 0.3737 hours

If for simplicity we take the rest stop at the start the total journey time is (0.3767 + t)
where t is the driving time.

If d is the distance travelled then speed =
d/t=85.6 km/h

However the average speed is from time zero, thus speed from time zero

is d/(t+0.3767)=61.6 km/h

Next step is to rearrange
d/t=85.6 km/h
with t as the subject and substitute in

d/(t+0.3767)=61.6 km/h

and solve for d

Hope this is OK.