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## Comment on

Nani’s Average Speed## If we take distance = 120

## Great approach. You chose an

Great approach. You chose an arbitrary distance (120 miles) between Nani's work and home and then made the necessary calculations. That works too!

## I didn't get the shortcut

## Notice that, in my solution,

Notice that, in my solution, the d variables cancel out at 2:23 in the video. In other words, the distance from home to work is irrelevant.

Given this, we might assign a "nice" value to the distance. A nice value will be one that works nicely with the 2 speeds (30 mph and 40 mph).

So, let's say 120 miles = the distance from home to work.

This mean TOTAL distance traveled = 120 miles TO work + 120 miles FROM work = 240 miles

Average speed = (TOTAL distance traveled)/(TOTAL travel time)

We're told the average speed for the ENTIRE TRIP was 30 mph.

So, we can write: 30 = (240)/(TOTAL travel time)

Solving the equation, we see that the TOTAL travel time must be 8 hours.

Time from home to work = distance/speed = (120 miles)/(40 mph) = 3 hours

This means the time from work to home = 8 hours - 3 hours = 5 hours

So, it took 5 hours from Nani to travel the 120 miles from home to work.

Speed from home to work = distance/time = 120/5 = 24 mph

## Another way to approach this

total travel time is 2d/30

travel time to work d/40

travel time from work = 2d/30 - d/40 = 5d/120

average speed from work to home = d/(time travelling home)

= d/(5d/120) = 120/5 = 24

## Perfect - well done!

Perfect - well done!