Question

A person takes a trip, driving with a constant
speed 89 km/h except for a 16.4 min rest stop.
If the person’s average speed is 75.1 km/h,
how much time is spent on the trip?
Answer in units of h

Answer 1

@theEric :) sorry to bother you..

Answer 2

Not a problem, @Data_LG2 !

I'll go through the concepts involved! If either of you have questions, I'll be happy to answer them until I go offline!

Now, speed is the distance per time, so direction doesn't matter. Everything amount we think of has no given direction, and so there is no positive or negative amount.

The average speed, which I'll label \(\bar v\), is the overall change in distance divided by the total change in time to achieve that distance. This would be the sum of the distance changes over the sum of time changes.

We could look at that like there's the distance it travels when it's moving and the time it takes then, and there's the distance it travels when it is stopped (zero) and the time it takes for that. I will use algebra, so the moving intervals have a subscript of \(1\) and the stationary intervals have a subscript of \(2\).

Math speaking, that is \(\bar v =\dfrac{\Delta d_1+\Delta d_2}{\Delta t_1+\Delta t_2}\).

Note that \(\Delta d_2=0\), so \(\Delta d_1+\Delta d_2=\Delta d_1\). I'll substitute that in later - you'll see the \(\Delta d_2\) go away.

Note that the \(\dfrac{\Delta d_1}{\Delta t_1}\) is the constant speed of 89 km/h.

Then, \(\dfrac{\Delta d_1}{\Delta t_1}=v\). Not \(\bar v\), though. Then \(\Delta d_1=v\ \Delta t_1\). Substituting that in for \(\Delta{d_1}\) gets us...

\(\bar v =\dfrac{v\ \Delta t_1}{\Delta t_1+\Delta t_2}\)
Let me highlight what we don't know:
\(\bar v =\dfrac{v\ \color{red}{\Delta t_1}}{\color{red}{\Delta t_1}+\Delta t_2}\)
So we have to solve for them or it!!

I did. But I did the physics, the algebra is the next step and I leave it for you.

Please try to understand what I was thinking with my physics. It will probably help!

Lastly, the total time of the trip is \(\Delta t_1+\Delta t_2\).

Remember that \(\Delta t_2\) is in minutes, and you want the answer in hours.