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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!