Question

a person takes a trip driving with a constant speed of 89.5 km/h except for a 22 min. rest stop. If the average speed is 77.8 km/h, how much time is spent on the trip and how far does the person travel

Answer 1

\[v _{avg} = \Delta x/\Delta t\]
the total time for the trip is the sum of the time for the stop (22 min) + the time for the travel at 89.5 km/h, or
\[\Delta t = 22/60 h + t _{89.5}\]
Since the average velocity including the stop is 77.8km/h, using teh formula for average velocity
\[77.8km/h = \Delta x/\Delta t = \Delta x/[(22/60) h + t _{89.5}]\]
rearranging
\[77.8 km/h*[(22/60)h + t _{89.5}] = \Delta x\]
We know the driver drove at 89.5 km/h for the entire distance (no distance covered while stopped), so
\[\Delta x = 89.5 km/h * t _{89.5}\]
set the two expressions for the distance equal to each other and solve for the time, then use that value to calculate the distance

Answer 2

Just to check if I did it correctly, does that make
19 minutes spent on the trip and
28.5 km (1dp) traveled?

Answer 3

If you know that much about his speed why didn't you just ask him what time he left and what time he arrived? The math is a lot easier.