Question regarding average velocity

[missequivocal]

Homework Statement

What is the average velocity if you drive a distance of 472.5 km at a speed of 40 km/h, then the same distance at a speed of 65 km/h? Answer in units of km/h.

Homework Equations

t = d / v

The Attempt at a Solution

11.8125 = 472.5 / 40
7.269230769 = 472.5 / 65



Not really sure where to go from here.
I've done a few of these equations before, I am just having a brain block and I need to submit the answer to this problem by tonight.

Someone just point me in the right direction. :P

 

[missequivocal]

Haha wow that was so simple. Finally remembered.
Got it. :P

 

[m2003]

I would approach this problem by first defining the terms and variables involved. Average velocity is defined as the total displacement divided by the total time taken. In this case, the total distance is 472.5 km and the total time is the sum of the individual times taken at each speed.

So, we can calculate the total time taken as follows:

t1 = 472.5 km / 40 km/h = 11.8125 hours
t2 = 472.5 km / 65 km/h = 7.269 hours

The total time taken is the sum of these two times:
t = t1 + t2 = 11.8125 hours + 7.269 hours = 19.0815 hours

Now, we can calculate the average velocity using the total distance and total time:
Average velocity = 472.5 km / 19.0815 hours = 24.773 km/h

Therefore, the average velocity for this trip is 24.773 km/h. This means that if you had traveled the entire distance at a constant speed of 24.773 km/h, it would have taken you the same amount of time as it did with the varying speeds of 40 km/h and 65 km/h.