# Question: Nani’s Average Speed

## Comment on Nani’s Average Speed

### If we take distance = 120

If we take distance = 120 miles (lcm of 30 and 40) and then total time must be 240/30 = 8hrs. Time while going = 120/40=3. Therefore time while coming back must be 5hrs. Hence speed would be 120/5=24miles/hr.

### 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

I didn't get the shortcut solution

### 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

Another way to approach this problem is to find the time it took Nani to travel from work to home and use that information to find her average speed travelling home.
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!